3,013 results
Search Results
2. Letter to the editor: on the paper 'The double Pareto-Lognormal distribution—a new parametric model for size distributions' and its correction
- Author
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Neven Grbac and Tihana Galinac Grbac
- Subjects
Statistics and Probability - Published
- 2023
3. Letter on the paper 'On the two-parameter Bell–Touchard discrete distribution'
- Author
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Pedro Puig
- Subjects
Statistics and Probability - Published
- 2022
4. A report on the paper 'Sungsu Kim. 2019. The probable error in the hypothesis test of normal means using a small sample. Communications in Statistics - Theory and Methods. DOI: 10.1080/03610926.2019.1703135.'
- Author
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K. Krishnamoorthy and Arvind Shah
- Subjects
Statistics and Probability ,Distribution (number theory) ,Statistics ,Sample (statistics) ,Small sample ,Statistical theory ,Probable error ,Statistic ,Statistical hypothesis testing ,Mathematics - Abstract
Let X1,…,Xn be a sample from a N(μ,σ2) distribution. Consider testing H0:μ=μ0 vs. Ha:μ>μ0 The usual t-test is based on the statistic t=X¯−μ0S/n where X¯=1n∑i=1nXi and S2=1n−1∑i=1n(Xi−X¯)2 Kim (2019...
- Published
- 2020
5. Correction to the paper 'A new extension of the FGM copula with an application in reliability' by Rasha Ebaid, Walid Elbadawy, Essam Ahmed & Abdalla Abdelghaly
- Author
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Haroon M. Barakat, M. A. Alawady, and M. A. Abd Elgawad
- Subjects
Statistics and Probability ,Discrete mathematics ,Copula (linguistics) ,Extension (predicate logic) ,Reliability (statistics) ,Mathematics - Abstract
Ebaid et al. (2020) proposed the following new extended FGM copula (1) C ( u , v ) = u v [ 1 + a ( 1 − u ) ( 1 − v ) ( 1 − b u ) ( 1 − b v ) ] , 0 ≤ b < 1. Ebaid et al. (2020) claimed that, the adm...
- Published
- 2021
6. A Remark on the Paper 'A Note on Directional Dependence in Regression Setting' By Engin A. Sungur
- Author
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M. V. Muddapur
- Subjects
Statistics and Probability ,Statistics ,Econometrics ,Regression analysis ,Regression ,Mathematics - Published
- 2008
7. On a paper by kageyama and mohan
- Author
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Peter W.M. John
- Subjects
Statistics and Probability ,Combinatorics ,Discrete mathematics ,Association scheme ,Series (mathematics) ,Group (mathematics) ,Incomplete block ,Incidence matrix ,Incomplete block design ,Special case ,Mathematics - Abstract
Kageyama Mohan (1984) have presented three methods of constructing new incomplete block designs from balanced incomplete block designs, They raise questions about the designs which come from each of their methods, These questions are answered, Another series of group divisible designs is derived as a special case of their second method.
- Published
- 1986
8. Optimum spring balance weighing designs for estimating the total weight
- Author
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Meena N. Swamy
- Subjects
Statistics and Probability ,Generalized inverse ,Statistics ,Spring scale ,Variance (accounting) ,Paper based ,Upper and lower bounds ,Mathematics - Abstract
The problem of estimation of the total weight or objects using a spring balance weighing design has been deait with in this paper Based on a theorem by Dey and Gupta (1977) giving a lower bound for the variance of the estimated total weight, a necessary and sufficient condition for this lower bound to be attained is obtained. A few special cases where the lower bound is attained are enumerated.
- Published
- 1980
9. Sequential specification tests to choose a model: A change-point approach
- Author
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Adam Sales
- Subjects
Methodology (stat.ME) ,FOS: Computer and information sciences ,Statistics and Probability ,Applications (stat.AP) ,Statistics - Applications ,Statistics - Methodology - Abstract
Researchers faced with a sequence of candidate model specifications must often choose the best specification that does not violate a testable identification assumption. One option in this scenario is sequential specification tests: hypothesis tests of the identification assumption over the sequence. Borrowing an idea from the change-point literature, this paper shows how to use the distribution of p-values from sequential specification tests to estimate the point in the sequence where the identification assumption ceases to hold. Unlike current approaches, this method is robust to individual errant p-values and does not require choosing a test level or tuning parameter. This paper demonstrates the method's properties with a simulation study, and illustrates it by application to the problems of choosing a bandwidth in a regression discontinuity design while maintaining covariate balance and of choosing a lag order for a time series model., Forthcoming in Communications in Statistics -- Theory and Methods
- Published
- 2023
10. On the dependence structure of the trade/no trade sequence of illiquid assets
- Author
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Ra��ssi, Hamdi
- Subjects
FOS: Economics and business ,Statistics and Probability ,Statistical Finance (q-fin.ST) ,FOS: Mathematics ,Quantitative Finance - Statistical Finance ,Mathematics - Statistics Theory ,Statistics Theory (math.ST) - Abstract
In this paper, we propose to consider the dependence structure of the trade/no trade categorical sequence of individual illiquid stocks returns. The framework considered here is wide as constant and time-varying zero returns probability are allowed. The ability of our approach in highlighting illiquid stock's features is underlined for a variety of situations. More specifically, we show that long-run effects for the trade/no trade categorical sequence may be spuriously detected in presence of a non-constant zero returns probability. Monte Carlo experiments, and the analysis of stocks taken from the Chilean financial market, illustrate the usefulness of the tools developed in the paper.
- Published
- 2022
11. Objective priors for common correlation coefficient in bivariate normal populations
- Author
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Sang Gil Kang, Woo Dong Lee, and Yongku Kim
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Statistics and Probability ,Correlation coefficient ,Prior probability ,Statistics ,Multivariate normal distribution ,macromolecular substances ,Bayesian inference ,Mathematics - Abstract
Various objective priors have been defined for the common correlation coefficient concerning several bivariate normal populations. In this paper, the proposed approach relies on the asymptotic matching of coverage probabilities corresponding to Bayesian credible intervals considering the corresponding frequentist ones. In the present paper, we focus on several matching criteria including quantile matching, distribution function matching, highest posterior density matching, and matching via inversion of test statistics. In addition, we consider reference priors for different groups of ordering. The proposed methods are investigated and compared between each other in terms of a frequentist coverage probability and then, they are illustrated through a simulation study and two real data examples.
- Published
- 2021
12. On monotonically proceeding structures and stepwise increasing transition matrices of Markov chains
- Author
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Philippe Carette, Marie-Anne Guerry, Data Analytics Laboratory, and Business technology and Operations
- Subjects
Statistics and Probability ,Markov chain ,monotonic evolution ,Stochastic matrix ,Monotonic function ,transition matrix ,Statistics and Probability. Markov chain ,Business and Economics ,eigenvector ,Markov chain, transition matrix, eigenvalue, eigenvector, monotonic evolution ,eigenvalue ,Transition matrices ,Statistical physics ,Eigenvalues and eigenvectors ,Mathematics - Abstract
In general, the transition matrix of a Markov chain is a stochastic matrix. For a system that is modeled by a Markov chain, the transition matrix must reflect the characteristics of that system. The present paper introduces a particular class of transition matrices in order to model Markov systems for which, as the length of the time interval becomes greater, a transition from one state to another is more likely. We call these transition matrices stepwise increasing. Moreover in some contexts it is less desirable that the stocks fluctuate over time. In those situations, one is interested in monotonically proceeding stock vectors. This paper examines monotonically proceeding stock vectors and stepwise increasing transition matrices. We present conditions on the transition matrix such that all stock vectors are monotonically proceeding. In particular, the set of monotonically proceeding vectors is characterized for the two-state and three-state cases.
- Published
- 2020
13. Robust two-level regular fractional factorial designs
- Author
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Runchu Zhang and Chao Chen
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Statistics and Probability ,Hierarchy (mathematics) ,Fractional factorial design ,Model quality ,Arithmetic ,Mathematics - Abstract
In this paper, we introduce the concept of model quality for two-level regular fractional factorial designs. Under the effect hierarchy principle, this paper raises the definition of model ...
- Published
- 2019
14. Sparse bayesian kernel multinomial probit regression model for high-dimensional data classification
- Author
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Lianjie Shu, Aijun Yang, Xuejun Jiang, and Pengfei Liu
- Subjects
Statistics and Probability ,Clustering high-dimensional data ,021103 operations research ,business.industry ,Bayesian probability ,0211 other engineering and technologies ,Feature selection ,Pattern recognition ,Regression analysis ,02 engineering and technology ,01 natural sciences ,010104 statistics & probability ,ComputingMethodologies_PATTERNRECOGNITION ,Kernel (statistics) ,Covariate ,Multinomial probit ,Artificial intelligence ,0101 mathematics ,business ,Mathematics ,Reproducing kernel Hilbert space - Abstract
In this paper we introduce a sparse Bayesian kernel multinomial probit regression model for multi-class cancer classification. The relationship between the cancer types and gene expression measurements is explained by an unknown function which belongs to an abstract functional space like the reproducing kernel Hilbert space. We assign a sparse prior for regression parameters and perform variable selection by indexing the covariates of the model with a binary vector. The correlation prior for the binary vector assigned in this paper is able to distinguish models with the same size. The proposed method is successfully tested on one simulated data set and two publicly available real life data sets.
- Published
- 2018
15. Wavelet-based estimators of multivariable mean regression function with long-memory data
- Author
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Yunzhu He and Dongsheng Wu
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Statistics and Probability ,Polynomial regression ,Statistics::Theory ,Multivariable calculus ,05 social sciences ,Estimator ,Function (mathematics) ,01 natural sciences ,Statistics::Computation ,Nonparametric regression ,010104 statistics & probability ,Wavelet ,0502 economics and business ,Statistics ,Piecewise ,Statistics::Methodology ,0101 mathematics ,Asymptotic expansion ,050205 econometrics ,Mathematics - Abstract
Wavelet analysis has been proved to be a powerful statistical technique in the non parametric regression. In this paper, we propose non linear wavelet-based estimators for multivariable mean regression function with long-memory data. We also provide an asymptotic expansion for the mean integrated squared error (MISE) of the function estimators. This MISE expansion still works even when the underlying mean regression function is only piecewise smooth. This paper extends the corresponding results in the literature for single variable to multivariable case.
- Published
- 2018
16. An analysis pipeline for estimating true intake from repeated measurements with random errors
- Author
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Jeongseon Kim, Woojoo Lee, and Seongil Jo
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Statistics and Probability ,Shrinkage estimator ,021103 operations research ,Nutritional epidemiology ,Accurate estimation ,Dietary intake ,Pipeline (computing) ,0211 other engineering and technologies ,02 engineering and technology ,Best linear unbiased prediction ,01 natural sciences ,010104 statistics & probability ,Random error ,Statistics ,0101 mathematics ,Mathematics - Abstract
The accurate estimation of an individual's usual dietary intake is an important topic in nutritional epidemiology. This paper considers the best linear unbiased predictor (BLUP) computed from repeatedly measured dietary data and derives several nonparametric prediction intervals for true intake. However, the performance of the BLUP and the validity of prediction intervals depends on whether required model assumptions for the true intake estimation problem hold. To address this issue, the paper examines how the BLUP and prediction intervals behave in the case of a violation of model assumptions, and then proposes an analysis pipeline for checking them with data.
- Published
- 2018
17. Bimodal symmetric-asymmetric power-normal families
- Author
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Hugo S. Salinas, Guillermo Martínez-Flórez, and Heleno Bolfarine
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Statistics and Probability ,Skew normal distribution ,Normalizing constant ,PROBABILIDADE ,Estimator ,02 engineering and technology ,01 natural sciences ,Normal distribution ,010104 statistics & probability ,symbols.namesake ,Skewness ,0202 electrical engineering, electronic engineering, information engineering ,symbols ,Calculus ,Kurtosis ,Applied mathematics ,020201 artificial intelligence & image processing ,0101 mathematics ,Fisher information ,Generalized normal distribution ,Mathematics - Abstract
This paper proposes new symmetric and asymmetric distributions applying methods analogous as the ones in Kim (2005) and Arnold et al. (2009) to the exponentiated normal distribution studied in Durrans (1992), that we call the power-normal (PN) distribution. The proposed bimodal extension, the main focus of the paper, is called the bimodal power-normal model and is denoted by BPN(α) model, where α is the asymmetry parameter. The authors give some properties including moments and maximum likelihood estimation. Two important features of the model proposed is that its normalizing constant has closed and simple form and that the Fisher information matrix is nonsingular, guaranteeing large sample properties of the maximum likelihood estimators. Finally, simulation studies and real applications reveal that the proposed model can perform well in both situations.
- Published
- 2017
18. Finding the maximum efficiency for multistage ranked-set sampling
- Author
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Jesse Frey and Timothy G. Feeman
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Statistics and Probability ,Generalization ,05 social sciences ,Sampling (statistics) ,Quantile function ,Simple random sample ,01 natural sciences ,010104 statistics & probability ,Ranking ,Bounded function ,0502 economics and business ,Statistics ,Sampling design ,Cluster sampling ,0101 mathematics ,050205 econometrics ,Mathematics - Abstract
Multistage ranked-set sampling (MRSS) is a generalization of ranked-set sampling in which multiple stages of ranking are used. It is known that for a fixed distribution under perfect rankings, each additional stage provides a gain in efficiency when estimating the population mean. However, the maximum possible efficiency for the MRSS sample mean relative to the simple random sampling sample mean has not previously been determined. In this paper, we provide a method for computing this maximum possible efficiency under perfect rankings for any choice of the set size and the number of stages. The maximum efficiency tends to infinity as the number of stages increases, and, for large numbers of stages, the efficiency-maximizing distributions are symmetric multi-modal distributions where the number of modes matches the set size. The results in this paper correct earlier assertions in the literature that the maximum efficiency is bounded and that it is achieved when the distribution is uniform.
- Published
- 2017
19. Bounded risk estimation of a linear combination of location parameters in negative exponential distributions via three-stage sampling
- Author
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Eiichi Isogai and Andreas Futschik
- Subjects
Statistics and Probability ,Estimation ,Work (thermodynamics) ,Scale (ratio) ,05 social sciences ,Sampling (statistics) ,01 natural sciences ,010104 statistics & probability ,Sample size determination ,Bounded function ,0502 economics and business ,Statistics ,Point estimation ,0101 mathematics ,Linear combination ,050205 econometrics ,Mathematics - Abstract
The paper deals with the problem of bounded risk point estimation for a linear combination of location parameters of two negative exponential distributions. Isogai and Futschik considered the situation when the location and scale parameters are all unknown. They proposed purely sequential procedures and gave second order expansions of the average sample sizes and risks. In this paper we propose three-stage procedures and derive second order expansions of the average sample sizes and risks. Further, we compare the results with those from previous work.
- Published
- 2017
20. Non-parametric predictive inference for future order statistics
- Author
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Hana N. Alqifari, Frank P. A. Coolen, and Tahani Coolen-Maturi
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Statistics and Probability ,Order statistic ,Nonparametric statistics ,Conditional probability ,02 engineering and technology ,01 natural sciences ,010104 statistics & probability ,Predictive inference ,Robustness (computer science) ,Multiple comparisons problem ,Statistics ,0202 electrical engineering, electronic engineering, information engineering ,Statistical inference ,020201 artificial intelligence & image processing ,Pairwise comparison ,0101 mathematics ,Mathematics - Abstract
This paper presents nonparametric predictive inference for future order statistics. Given data consisting of n real-valued observations, m future observations are considered and predictive probabilities are presented for the r-th ordered future observation. In addition, joint and conditional probabilities for events involving multiple future order statistics are presented. The paper further presents the use of such predictive probabilities for order statistics in statistical inference, in particular considering pairwise and multiple comparisons based on two or more independent groups of data.
- Published
- 2017
21. Stepanov-like almost automorphic solutions for stochastic differential equations with Lévy noise
- Author
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Litan Yan, Liping Xu, and Zhi Li
- Subjects
Statistics and Probability ,Class (set theory) ,010102 general mathematics ,Mathematical analysis ,Poisson distribution ,01 natural sciences ,010101 applied mathematics ,Stochastic differential equation ,symbols.namesake ,Levy noise ,Exponential stability ,symbols ,Applied mathematics ,Uniqueness ,0101 mathematics ,Mathematics - Abstract
In this paper, we introduce a new concept of Poisson Stepanov-like almost automorphy (or Poisson S2-almost automorphy). Under some suitable conditions on the coefficients, we establish the existence and uniqueness of Stepanov-like almost automorphic mild solution to a class of semilinear stochastic differential equations with infinite dimensional Levy noise. We further discuss the global asymptotic stability of these solution. Finally, we give an example to illustrate the theoretical results obtained in this paper.
- Published
- 2017
22. Statistical test based on intuitionistic fuzzy hypotheses
- Author
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Mohamad Ghasem Akbari and Gholamreza Hesamian
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Statistics and Probability ,education.field_of_study ,Relation (database) ,Mathematics::General Mathematics ,Population ,Nonparametric statistics ,02 engineering and technology ,01 natural sciences ,Test (assessment) ,010104 statistics & probability ,Statistics ,0202 electrical engineering, electronic engineering, information engineering ,Calculus ,020201 artificial intelligence & image processing ,p-value ,0101 mathematics ,education ,Type I and type II errors ,Statistical hypothesis testing ,Parametric statistics ,Mathematics - Abstract
In this paper, the classical statistical test based on intuitionistic fuzzy hypotheses in relation to the underlying population parametric is extended. In this approach, the type-I, type-II, power of test, and p-value are extended for intuitionistic fuzzy hypotheses. Throughout the paper, some applied examples are provided for both parametric and non parametric cases to clarify the discussions.
- Published
- 2017
23. Vine copula constructions of higher-dimensional dependent reliability systems
- Author
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Jingyuan Shen, Zhongping Li, Liying Wang, and Xujie Jia
- Subjects
Statistics and Probability ,Mathematical optimization ,021103 operations research ,Dimensionality reduction ,Copula (linguistics) ,0211 other engineering and technologies ,Multivariate normal distribution ,Statistics::Other Statistics ,02 engineering and technology ,Bivariate analysis ,01 natural sciences ,Statistics::Computation ,Vine copula ,010104 statistics & probability ,Cascade ,Statistics::Methodology ,0101 mathematics ,Mathematics - Abstract
Copulas have proved to be very successful tools for the flexible modeling of dependence. Bivariate copulas have been deeply researched in recent years, while building higher-dimensional copulas is still recognized to be a difficult task. In this paper, we study the higher-dimensional dependent reliability systems using a type of decomposition called “vine,” by which a multivariate distribution can be decomposed into a cascade of bivariate copulas. Some equations of system reliability for parallel, series, and k-out-of-n systems are obtained and then decomposed based on C-vine and D-vine copulas. Finally, a shutdown system is considered to illustrate the results obtained in the paper.
- Published
- 2017
24. Performance analysis of queue with two-stage vacation policy
- Author
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Qingqing Ye and Liwei Liu
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Statistics and Probability ,Waiting time ,Mathematical optimization ,021103 operations research ,0211 other engineering and technologies ,02 engineering and technology ,Limiting ,01 natural sciences ,010104 statistics & probability ,Distribution (mathematics) ,Renewal theory ,Stage (hydrology) ,0101 mathematics ,Working vacation ,Queue ,Mathematics - Abstract
In this paper, we investigate an M/M/1 queue with a two-stage vacation policy which comprises of single working vacation and single vacation. Using the matrix-analytic method, we obtain the distribution of stationary system size, and then the decomposition structures of the stationary system size and the sojourn time are demonstrated. Furthermore, we study the waiting time by first-passage time analysis. Meanwhile, the busy-cycle analysis is provided by the limiting theorem of alternative renewal process. Finally, several numerical examples are presented in the paper.
- Published
- 2017
25. Elasticity function of a discrete random variable and its properties
- Author
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Jose M. Pavía and Ernesto J. Veres-Ferrer
- Subjects
Statistics and Probability ,Mathematical optimization ,021103 operations research ,Discretization ,Hazard ratio ,0211 other engineering and technologies ,02 engineering and technology ,01 natural sciences ,Elasticity of a function ,Continuous variable ,010104 statistics & probability ,Applied mathematics ,Probability distribution ,0101 mathematics ,Elasticity (economics) ,Random variable ,Mathematics - Abstract
Elasticity (or elasticity function) is a new concept that allows us to characterize the probability distribution of any random variable in the same way as characteristic functions and hazard and reverse hazard functions do. Initially defined for continuous variables, it was necessary to extend the definition of elasticity and study its properties in the case of discrete variables. A first attempt to define discrete elasticity is seen in Veres-Ferrer and Pavia (2014a). This paper develops this definition and makes a comparative study of its properties, relating them to the properties shown by discrete hazard and reverse hazard, as both defined in Chechile (2011). Similar to continuous elasticity, one of the most interesting properties of discrete elasticity focuses on the rate of change that this undergoes throughout its support. This paper centers on the study of the rate of change and develops a set of properties that allows us to carry out a detailed analysis. Finally, it addresses the calculati...
- Published
- 2017
26. The Lamé class of Lorenz curves
- Author
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Vanesa Jordá, Carmen Trueba, José María Sarabia, and Universidad de Cantabria
- Subjects
Statistics and Probability ,Limited information ,Cumulative distribution function ,05 social sciences ,Mathematical analysis ,Lorenz curves ,Single parameter ,Donaldson-Weymark-Kakwan ,Gini ,0502 economics and business ,Pietra and Wolfson indices ,Economic model ,050207 economics ,Lorenz curve ,Estimation methods ,050205 econometrics ,Mathematics - Abstract
In this paper, the class of Lamé Lorenz curves is studied. This family has the advantage of modeling inequality with a single parameter. The family has a double motivation: it can be obtain from an economic model and from simple transformations of classical Lorenz curves. The underlying cumulative distribution functions have a simple closed form, and correspond to the Singh-Maddala and Dagum distributions, which are well known in the economic literature. The Lorenz order is studied and several inequality and polarization measures are obtained, including Gini, Donaldson-Weymark-Kakwani, Pietra and Wolfson indices. Some extensions of the Lamé family are obtained. Fitting and estimation methods under two different data configuration are proposed. Empirical applications with real data are given. Finally, some relationships with other curves are included. The authors thank to Ministerio de Econom a y Competitividad, project ECO2010-15455, for partial support. The second author thanks to the Ministerio de Educaci on (FPU AP-2010-4907) for partial support. We are grateful for the constructive suggestions provided by the reviewers, which improved the paper.
- Published
- 2017
27. Bayesian ratemaking under Dirichlet process mixtures
- Author
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Jinlong Huang, Jianjun Zhang, and Xianyi Wu
- Subjects
Statistics and Probability ,Mathematical optimization ,050208 finance ,05 social sciences ,Bayesian probability ,Conditional expectation ,01 natural sciences ,Conjugate prior ,Dirichlet process ,010104 statistics & probability ,symbols.namesake ,0502 economics and business ,Prior probability ,Econometrics ,symbols ,Portfolio ,0101 mathematics ,Parametric family ,Mathematics ,Gibbs sampling - Abstract
Experience ratemaking plays a crucial role in general insurance in determining future premiums of individuals in a portfolio by assessing observed claims from the whole portfolio. This paper investigates this problem in which claims can be modeled by certain parametric family of distributions. The Dirichlet process mixtures are employed to model the distributions of the parameters so as to make two advantages: to produce exact Bayesian experience premiums for a class of premium principles generated from generic error functions and, at the same time, provide robust and flexible ways to avoid possible bias caused by traditionally used priors such as non informative priors or conjugate priors. In this paper, the Bayesian experience ratemaking under Dirichlet process mixture models are investigated and due to the lack of analytical forms of the conditional expectations of the quantities concerned, the Gibbs sampling schemes are designed for the purpose of approximations.
- Published
- 2016
28. Complete moment convergence and Lr convergence for asymptotically almost negatively associated random variables
- Author
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Mengmei Xi, Junjie Lin, Ming Wang, Xufei Tang, and Xuejun Wang
- Subjects
Statistics and Probability ,Dominated convergence theorem ,Normal convergence ,010102 general mathematics ,01 natural sciences ,Combinatorics ,Moment (mathematics) ,010104 statistics & probability ,Convergence of random variables ,Convergence (routing) ,Proofs of convergence of random variables ,Applied mathematics ,Convergence tests ,0101 mathematics ,Random variable ,Mathematics - Abstract
In this paper, we investigate the complete moment convergence and Lr convergence for maximal partial sums of asymptotically almost negatively associated random variables under some general conditions. The results obtained in the paper generalize some corresponding ones for negatively associated random variables.
- Published
- 2016
29. Asymptotic properties of the maximum-likelihood estimator in zero-inflated binomial regression
- Author
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Alpha Oumar Diallo, Jean-François Dupuy, Aliou Diop, laboratoire d'Etudes et de recherches en Statistiques et Développement ( LERSTAD ), Université Gaston Bergé Sénégal, Institut de Recherche Mathématique de Rennes ( IRMAR ), Université de Rennes 1 ( UR1 ), Université de Rennes ( UNIV-RENNES ) -Université de Rennes ( UNIV-RENNES ) -AGROCAMPUS OUEST-École normale supérieure - Rennes ( ENS Rennes ) -Institut National de Recherche en Informatique et en Automatique ( Inria ) -Institut National des Sciences Appliquées ( INSA ) -Université de Rennes 2 ( UR2 ), Université de Rennes ( UNIV-RENNES ) -Centre National de la Recherche Scientifique ( CNRS ), Institut National des Sciences Appliquées - Rennes ( INSA Rennes ), laboratoire d'Etudes et de recherches en Statistiques et Développement (LERSTAD), Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-École normale supérieure - Rennes (ENS Rennes)-Université de Rennes 2 (UR2)-Centre National de la Recherche Scientifique (CNRS)-INSTITUT AGRO Agrocampus Ouest, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro), Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA), AGROCAMPUS OUEST, Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement (Institut Agro)-Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Université de Rennes 2 (UR2), Université de Rennes (UNIV-RENNES)-École normale supérieure - Rennes (ENS Rennes)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), and Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)
- Subjects
Statistics and Probability ,Statistics::Theory ,Binomial (polynomial) ,excess of zeros ,Binomial regression ,Asymptotic distribution ,01 natural sciences ,010104 statistics & probability ,[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] ,Consistency (statistics) ,0502 economics and business ,Statistics ,Consistent estimator ,Asymptotic normality ,Statistics::Methodology ,[ MATH.MATH-ST ] Mathematics [math]/Statistics [math.ST] ,0101 mathematics ,050205 econometrics ,Mathematics ,consistency ,05 social sciences ,Estimator ,Regression analysis ,count data ,Statistics::Computation ,simulations ,Count data - Abstract
International audience; The zero-inflated binomial (ZIB) regression model was proposed to account for excess zeros in binomial regression. Since then, the model has been applied in various fields, such as ecology and epidemiology. In these applications, maximum-likelihood estimation (MLE) is used to derive parameter estimates. However, theoretical properties of the MLE in ZIB regression have not yet been rigorously established. The current paper fills this gap and thus provides a rigorous basis for applying the model. Consistency and asymptotic normality of the MLE in ZIB regression are proved. A consistent estimator of the asymptotic variance-covariance matrix of the MLE is also provided. Finite-sample behavior of the estimator is assessed via simulations. Finally, an analysis of a data set in the field of health economics illustrates the paper.
- Published
- 2016
30. On entropy of a Pareto distribution in the presence of outliers
- Author
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E. Khaleghpanah Nooghabi and M. Jabbari Nooghabi
- Subjects
Statistics and Probability ,Pareto interpolation ,Kullback–Leibler divergence ,Principle of maximum entropy ,02 engineering and technology ,01 natural sciences ,Rényi entropy ,010104 statistics & probability ,symbols.namesake ,Maximum entropy probability distribution ,Statistics ,0202 electrical engineering, electronic engineering, information engineering ,symbols ,Econometrics ,Entropy (information theory) ,020201 artificial intelligence & image processing ,Lomax distribution ,Pareto distribution ,0101 mathematics ,Mathematics - Abstract
The aim of this paper is obtaining the amount of information there exists in the Pareto distribution in the presence of outliers. For the sake of this purpose, Shannon entropy, ϵ-entropy, Fisher information, and Kullback–Leibler distance are computed. Furthermore, a section has been devoted to compare these quantities in these two cases of the Pareto distribution (with outliers and the homogenous case). At the end of this paper, two actual examples, which are related to insurance companies, are brought. A brief summary of which is done in this work is also reported.
- Published
- 2016
31. The effect of sample size and missingness on inference with missing data
- Author
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Morimoto, Julian
- Subjects
Statistics and Probability ,FOS: Mathematics ,Statistics::Methodology ,Mathematics - Statistics Theory ,Statistics Theory (math.ST) - Abstract
When are inferences (whether Direct-Likelihood, Bayesian, or Frequentist) obtained from partial data valid? This paper answers this question by offering a new asymptotic theory about inference with missing data that is more general than existing theories. It proves that as the sample size increases and the extent of missingness decreases, the average-loglikelihood function generated by partial data and that ignores the missingness mechanism will converge in probability to that which would have been generated by complete data; and if the data are Missing at Random, this convergence depends only on sample size. Thus, inferences from partial data, such as posterior modes, confidence intervals, likelihood ratios, test statistics, and indeed, all quantities or features derived from the partial-data loglikelihood function, will be consistently estimated. Additionally, the missing data mechanism has asymptotically no effect on parameter estimation and hypothesis testing if the data are Missing at Random. This adds to previous research which has only proved the consistency and asymptotic normality of the posterior mode. Practical implications are discussed, and the theory is illustrated through simulation using a previous study of International Human Rights Law., Submitted
- Published
- 2022
32. Comment on a generalized stochastic restricted ridge regression estimator
- Author
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Issam Dawoud, Selahattin Kaçıranlar, and Çukurova Üniversitesi
- Subjects
Generalized stochastic restricted ridge regression estimator ,Statistics and Probability ,Regression estimator ,Ridge (differential geometry) ,01 natural sciences ,010101 applied mathematics ,010104 statistics & probability ,Linear regression model ,Multicollinearity ,Statistics ,Linear regression ,0101 mathematics ,Mathematics - Abstract
In this note, we make some comments about the paper of Alheety and Kibria (2014) and correct the wrongly proved Theorems in that paper. © 2017 Taylor & Francis Group, LLC.
- Published
- 2016
33. Properties of the elasticity of a continuous random variable. A special look at its behavior and speed of change
- Author
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Ernesto J. Veres-Ferrer and Jose M. Pavía
- Subjects
Statistics and Probability ,021103 operations research ,Stochastic process ,0211 other engineering and technologies ,Failure rate ,02 engineering and technology ,01 natural sciences ,Elasticity of a function ,010104 statistics & probability ,symbols.namesake ,Econometrics ,symbols ,Probability distribution ,0101 mathematics ,Elasticity (economics) ,Fisher information ,Random variable ,Mathematics - Abstract
Belzunce et al. (1995) define the elasticity for non negative random variables as the reversed proportional failure rate (RPFR). Veres-Ferrer and Pavia (2012, 2014b) interpret it in economic terms, extending its definition to variables that can also take negative values, and briefly present the role of elasticity in characterizing probability distributions. This paper highlights a set of properties demonstrated by elasticity, which shows many similar properties to the reverse hazard function. This paper pays particular attention to studying the increase/decrease and the speed of change of the elasticity function. These are important properties because of the characterizing role of elasticity, which makes it possible to introduce our hypotheses and knowledge about the random process in a more meaningful and intuitive way. As a general rule, it is observed the need for distinguishing between positive and negative areas of the support.
- Published
- 2016
34. An adept-stratified Kuk's randomized response model using Neyman allocation
- Author
-
Tanveer A. Tarray and Housila P. Singh
- Subjects
010101 applied mathematics ,Statistics and Probability ,010104 statistics & probability ,Statistics ,Econometrics ,Randomized response ,0101 mathematics ,01 natural sciences ,Stratified sampling ,Mathematics - Abstract
This paper suggests a new stratified randomized response model based on Kuk's [Biometrika (1990), 77, 2, pp.436–438] model that has Neyman allocation and considerable gain in precision. It has been identified that the stratified randomized response models due to Kim and Warde (2004), Kim and Elam's (2005), and Kim and Elam's (2007) are members of the proposed model. It is shown that the proposed model is more efficient than Kuk's (1990) model both theoretically and empirically. The results of this paper are also extended in the situation when trials are repeated.
- Published
- 2016
35. On discrete-time stable multiple Markov processes
- Author
-
M. Taghipour and Alireza Nematollahi
- Subjects
Statistics and Probability ,Markov kernel ,Markov chain ,Variable-order Markov model ,Markov process ,Markov model ,Time reversibility ,Combinatorics ,symbols.namesake ,Markov renewal process ,symbols ,Applied mathematics ,Markov property ,Mathematics - Abstract
In this paper, we provide necessary conditions for discrete-time symmetric α-stable processes to be linear 2-ple Markov. The aim of this paper is to extend the results given by Adler et al. (1990) ...
- Published
- 2016
36. High-dimensional posterior consistency of the Bayesian lasso
- Author
-
Shibasish Dasgupta
- Subjects
Statistics and Probability ,05 social sciences ,Bayesian probability ,01 natural sciences ,Statistics::Computation ,Bayesian statistics ,010104 statistics & probability ,Frequentist inference ,Consistency (statistics) ,0502 economics and business ,Econometrics ,Bayesian experimental design ,Statistics::Methodology ,Bayesian hierarchical modeling ,0101 mathematics ,Bayesian linear regression ,Bayesian average ,Algorithm ,050205 econometrics ,Mathematics - Abstract
This paper considers posterior consistency in the context of high-dimensional variable selection using the Bayesian lasso algorithm. In a frequentist setting, consistency is perhaps the most basic property that we expect any reasonable estimator to achieve. However, in a Bayesian setting, consistency is often ignored or taken for granted, especially in more complex hierarchical Bayesian models. In this paper, we have derived sufficient conditions for posterior consistency in the Bayesian lasso model with the orthogonal design, where the number of parameters grows with the sample size.
- Published
- 2016
37. Asymptotic Inferences for an AR(1) Model with a Change Point and Possibly Infinite Variance
- Author
-
Danna Zhang and Tianxiao Pang
- Subjects
Statistics and Probability ,Combinatorics ,Sequence ,Indicator function ,Autoregressive model ,Domain (ring theory) ,Statistics ,Estimator ,Asymptotic distribution ,Least squares ,Random variable ,Mathematics - Abstract
The basic model in this paper is an AR(1) model with a structural break in the AR parameter β at an unknown time k0. That is, yt = β1yt − 1I{t ⩽ k0} + β2yt − 1I{t > k0} + ϵt, t = 1, 2, ⋅⋅⋅, T, where I{ · } denotes the indicator function. Suppose |β1| < 1, |β2| < 1, and {ϵt, t ⩾ 1} is a sequence of i.i.d. random variables which are in the domain of attraction of the normal law with zero mean and possibly infinite variance, then the limiting distributions for the least squares estimators of β1 and β2 are studied in the present paper, which extend some results in Chong (2001).
- Published
- 2015
38. Binomial Mixture Modeling of University Credits
- Author
-
Leonardo Grilli, Roberta Varriale, and Carla Rampichini
- Subjects
Statistics and Probability ,Binomial (polynomial) ,Distribution (number theory) ,Exploit ,Model selection ,Physics::Physics Education ,Test (assessment) ,Multimodality ,Variable (computer science) ,Econometrics ,TUTOR ,computer ,computer.programming_language ,Mathematics - Abstract
The paper reviews finite mixture models for binomial counts with concomitant variables. These models are well known in theory, but they are rarely applied. We use a binomial finite mixture to model the number of credits gained by freshmen during the first year at the School of Economics of the University of Florence. The finite mixture approach allows us to appropriately account for the large number of zeroes and the multimodality of the observed distribution. Moreover, we rely on a concomitant variable specification to investigate the role of student background characteristics and of a compulsory pre-enrollment test in predicting gained credits. In the paper, we deal with model selection, including the choice of the number of components, and we devise numerical and graphical summaries of the model results in order to exploit the information content of the concomitant variable specification. The main finding is that the introduction of the pre-enrollment test gives additional information for student tutor...
- Published
- 2015
39. Uniform Asymptotic Estimates for Ruin Probabilities with Exponential Lévy Process Investment Returns and Two-sided Linear Heavy-tailed Claims
- Author
-
Dingcheng Wang and Fenglong Guo
- Subjects
Statistics and Probability ,Independent and identically distributed random variables ,Actuarial science ,Heavy-tailed distribution ,Econometrics ,Portfolio ,First-hitting-time model ,Investment (macroeconomics) ,Ruin theory ,Lévy process ,Mathematics ,Exponential function - Abstract
This paper investigates the ruin probabilities of a renewal risk model with stochastic investment returns and dependent claim sizes. The investment is described as a portfolio of one risk-free asset and one risky asset whose price process is an exponential Levy process. The claim sizes are assumed to follow a two-sided linear process with independent and identically distributed step sizes. When the step-size distribution is heavy tailed, the paper establishes some uniform asymptotic formulas of ruin probabilities.
- Published
- 2015
40. A discrete probability problem in card shuffling
- Author
-
Haimeng Zhang, Fu-Chih Cheng, Chunfeng Huang, and M. Bhaskara Rao
- Subjects
Statistics and Probability ,Recurrence relation ,Shuffling ,Markov chain ,010102 general mathematics ,Probabilistic logic ,Process (computing) ,01 natural sciences ,Table (database) ,0101 mathematics ,Line (text file) ,Arithmetic ,Algorithm ,Mathematics - Abstract
There are n cards serially numbered from 1 to n. The cards are shuffled and placed in a line one after the other on top of a table with faces up. The numbers on the faces are read from left to right. If there are consecutive numbers in increasing order of magnitude the corresponding cards are merged into one. After the merger, the cards are numbered serially from one to whatever the number of cards we now have. The cards are shuffled and placed in a line one after another on top of the table with faces up. The process continues until we have only one card left. In this paper, we develop a probabilistic recurrence relation approach to obtain the mean, variance, and distribution of the number of shuffles needed. A Markov chain formulation and its properties are discussed in the paper as well.
- Published
- 2015
41. Multiple Comparisons with Control Under Stochastic Ordering: Controlling FDR
- Author
-
Jinde Wang and Jianwei Gou
- Subjects
Statistics and Probability ,False discovery rate ,Controllability ,Location test ,Multiple comparisons problem ,Control (management) ,Probability distribution ,Stochastic ordering ,Algorithm ,Test (assessment) ,Mathematics - Abstract
Multiple comparisons of the effects of several treatments with a control (MCC) has been a central problem in medicine and other areas. Nearly all of existing papers are devoted to comparing means of the effects. To study medical problems more deeply, one needs more information than mean relationship from the given data. It can be expected to get more useful and deeper conclusion by comparing the probability distributions, i.e., by comparison under stochastic orders. This paper presents a likelihood ratio testing procedure to compare effects under stochastic order for MCC problems, controlling the false discovery rate (FDR). Setting a test controlling FDR under stochastic order faces several non trivial problems. These problems are analyzed and solved in this paper. To facilitate the test more easily, the asymptotic p values for the test are used and their distributions are derived. It is shown that controllability of FDR for this comparison procedure can be guaranteed. A real data example is used to illus...
- Published
- 2015
42. The Pearson Score Statistic for Multinomial-Poisson Models
- Author
-
Joseph B. Lang
- Subjects
Statistics and Probability ,Contingency table ,symbols.namesake ,One- and two-tailed tests ,Sampling distribution ,Statistics ,Ancillary statistic ,Pearson's chi-squared test ,symbols ,Test statistic ,Completeness (statistics) ,Sufficient statistic ,Mathematics - Abstract
The score statistic S2 is commonly used for general likelihood-based inference. Pearson’s Chi-squared statistic X2 = ∑(O − E)2/E is ubiquitous in contingency table inference. Because tests and confidence intervals based on S2 have been shown to work well in practice and theory and because X2 has such a simple and intuitively appealing form, it is of interest to know when S2 is identical to X2 and when X2 has an approximate Chi-squared distribution. Toward these ends, this paper gives a simple proof that S2 = X2 for the broad class of multinomial-Poisson distributions when the alternative hypothesis is unrestricted in a certain sense. This paper also gives a sufficient condition under which the null distribution of the Pearson score statistic is approximately Chi-squared. Several examples illustrate the utility of the results and counter-examples highlight the importance of the sufficient conditions of the results.
- Published
- 2014
43. A Proportional Hazard Marshall–Olkin Extended Family of Distributions and its Application to Gompertz Distribution
- Author
-
M. E. Ghitany, Ramesh C. Gupta, and R. A. Al-Jarallah
- Subjects
Statistics and Probability ,Hazard (logic) ,Bathtub ,Gompertz function ,Order statistic ,Statistics ,Extended family ,Failure rate ,Monotonic function ,Gompertz distribution ,Mathematics - Abstract
In this paper, we have presented a proportional hazard version of the Marshall–Olkin extended family of distributions. This family of distributions has been compared in terms of stochastic orderings with the Marshall-Olkin extended family of distributions. Considering the Gompertz distribution as the baseline, the monotonicity of the resulting failure rate is shown to be either increasing or bathtub, even though the Gompertz distribution has an increasing failure rate. The maximum likelihood estimation of the parameters has been studied and a data set, involving the serum–reversal times, has been analyzed and it has been shown that the model presented in this paper fit better than the Gompertz or even the Mrashall–Olkin Gompertz distribution. The extension presented in this paper can be used in other family of distributions as well.
- Published
- 2014
44. Tail Probability Ratios of Normal and Student’stDistributions
- Author
-
Tiejun Tong and Heng Peng
- Subjects
Statistics and Probability ,Combinatorics ,Normal distribution ,Q-function ,Student's t-distribution ,Upper and lower bounds ,Mathematics ,T-tail - Abstract
The ratio of normal tail probabilities and the ratio of Student’s t tail probabilities have gained an increased attention in statistics and related areas. However, they are not well studied in the literature. In this paper, we systematically study the functional behaviors of these two ratios. Meanwhile, we explore their difference as well as their relationship. It is surprising that the two ratios behave very different to each other. Finally, we conclude the paper by conducting some lower and upper bounds for the two ratios.
- Published
- 2014
45. Modified see variable selection for linear instrumental variable regression models
- Author
-
Peixin Zhao and Liugen Xue
- Subjects
Statistics and Probability ,Mathematical optimization ,Linear regression ,Covariate ,Instrumental variable ,Linear model ,Econometrics ,Regression analysis ,Feature selection ,Estimating equations ,Endogeneity ,Mathematics - Abstract
This paper considers the problem of variable selection for a class of linear regression models with instrumental variables. We focus on the case that the covariates are endogenous variables, and some auxiliary instrumental variables are available. An instrumental variable based variable selection procedure is proposed by using a modified smooth-threshold estimating equations (SEE). The proposed method can attenuate the effect of endogeneity of covariates, and can avoid the convex optimization problem. Hence, it is flexible and easy to implement. Simulation results indicate that the proposed variable selection method is workable.
- Published
- 2022
46. A Generalized General Minimum Lower Order Confounding Criterion for General Orthogonal Designs
- Author
-
Runchu Zhang and Yi Cheng
- Subjects
Statistics and Probability ,Optimal design ,Mathematical optimization ,Efficient algorithm ,Confounding ,Applied mathematics ,Lower order ,Base (topology) ,Frequency vector ,Mathematics - Abstract
In this paper, we extend the AENP and the GMC criterion proposed by Zhang et al. (2008) to the case of nonregular orthogonal designs. A G-AENP and correspondingly a G-GMC criterion are proposed. The confounding frequency vector (CFV) and the generalized wordlength pattern (GWLP), as the base of MGA and GMA criteria, are shown to be functions of the G-AENP. Some optimal properties of G-GMC designs are obtained. At the last, we give an efficient algorithm for finding optimal designs and tabulate some G-GMC designs with 16- and 18-run for application and comparison with GMA and MGA designs.
- Published
- 2022
47. Non Parametric Regression Quantile Estimation for Dependent Functional Data under Random Censorship: Asymptotic Normality
- Author
-
Walid Horrigue and Elias Ould Saïd
- Subjects
Statistics and Probability ,Statistics::Theory ,Estimator ,Asymptotic distribution ,Quantile function ,Censoring (statistics) ,Quantile regression ,Nonparametric regression ,Kernel (statistics) ,Statistics ,Econometrics ,Statistics::Methodology ,Quantile ,Mathematics - Abstract
In this paper we study a smooth estimator of the regression quantile function in the censorship model when the covariates take values in some abstract function space. The main goal of this paper is to establish the asymptotic normality of the kernel estimator of the regression quantile, under α-mixing condition and, on the concentration properties on small balls probability measure of the functional regressors. Some applications and particular cases are studied. This study can be applied in time series analysis to the prediction and building confidence bands. Some simulations are drawn to lend further support to our theoretical results and to compare the quality of behavior of the estimator for finite samples with different rates of censoring and sizes.
- Published
- 2014
48. Bayesian Survival Analysis of Head and Neck Cancer Data Using Lognormal Model
- Author
-
Puneet Srivastava, Radhey S. Singh, Satyanshu K. Upadhyay, and Puja Makkar
- Subjects
Statistics and Probability ,symbols.namesake ,Bayes' theorem ,Survival function ,Markov chain ,Bayesian probability ,Prior probability ,Monte Carlo method ,Statistics ,symbols ,Survival analysis ,Gibbs sampling ,Mathematics - Abstract
The paper considers a lognormal model for the survival times and obtains a Bayes solution by means of Gibbs sampler algorithm when the priors for the parameters are vague. The formulation given in the paper is mainly focused for censored data problems though it is equally well applicable for complete data scenarios as well. For the purpose of numerical illustration, we considered two real data sets on head and neck cancer patients when they have been treated using either radiotherapy or chemotherapy followed by radiotherapy. The paper not only compares the survival functions for the two therapies assuming a lognormal model but also provides a model compatibility study based on predictive simulation results so that the choice of lognormal model can be justified for the two data sets. The ease of our analysis as compared to an earlier approach is certainly an advantage.
- Published
- 2013
49. Robust estimation of panel data regression models and applications
- Author
-
Ji, Ai-bing, Wei, Bo-wen, and Xu, Lan-ying
- Subjects
Statistics and Probability - Abstract
The common parameter estimation methods of panel data linear model include least square dummy variable estimation, two-stage least square estimation, quasi-maximum likelihood estimation and generalized moment estimation. However, these estimation methods are not robust and are easily affected by outliers. Firstly, this paper extends support vector regression algorithm to fit several parallel super-plane simultaneously and provide a novel robust estimation of fixed-effect panel data linear model; then using the kernel trick, a robust estimation for fixed effect panel data nonlinear model is introduced. Finally, the proposed model (linear or nonlinear) is applied in forecasting air quality index of the cities of Jing-Jin-Ji district in China. Experiments shows that our proposed model are robust and have good generalization performance.
- Published
- 2022
50. Measurement error in linear regression models with fat tails and skewed errors
- Author
-
Mahmoud Torabi, Jiyoun Myung, Mark F. J. Steel, and Malay Ghosh
- Subjects
Statistics and Probability ,Observational error ,High Energy Physics::Lattice ,05 social sciences ,Statistics::Other Statistics ,Bayesian inference ,01 natural sciences ,010104 statistics & probability ,13. Climate action ,Skewness ,Student's t-distribution ,0502 economics and business ,Linear regression ,Statistics ,0101 mathematics ,QA ,050205 econometrics ,Mathematics - Abstract
Linear regression models which account for skewed error distributions with fat tails have been previously studied. These two important features, skewness, and fat tails, are often observed in real data analyses. Covariates measured with an error also happen frequently in the observational data set-up. As a motivating example, wind speed as a covariate is usually used, among other covariates, to estimate the particulate matter (PM) which is one of the most critical air pollutants and has a major impact on human health and on the environment. However, the wind speed is measured with error and the distribution of PM is neither symmetric nor normally distributed (see Section “PM data application in Canada” for more details). Ignoring the issue of measurement error in covariates may produce bias in model parameters estimate and lead to wrong conclusions. In this paper, we propose an approach to study properly linear regression models where the covariates are measured with error and the error distribution is skewed with fat tails. We use a hierarchical Bayesian approach for inference, addressing also sensitivity of the results to priors. Performance of the proposed approach is evaluated through a simulation study and also by a real data application (PM in Canada).
- Published
- 2021
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