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Note, for instance, that the probabilities given by Castellares et al. ([1]) in page 4 are the same than those shown in expression (9.115) in the book by Johnson et al. ([3]), with the change of parameters Graph HT ht and Graph HT ht Neyman type A (NTA) distribution is frequently used in Biology, Biodosimetry, Environmental Sciences, Epidemiology, etc. A count random variable I X i is said to follow a stopped-sum Poisson, compound Poisson, multiple Poisson or clustered-Poisson distribution, if it can be represented as Graph HT ht where I N i is a Poisson random variable with parameter Graph HT ht and Graph HT ht are independent, identically distributed random variables that are also independent of I N i . [Extracted from the article]

Persuasive gamified systems are effective tools for motivating behaviour change using various persuasive strategies. In line with the reinforcement theory, some persuasive gamified systems employ reward and punishment in their design to achieve the intended behavioural outcome. Research has argued both in favour and against using these strategies in behaviour change applications due to mixed results with respect to their effectiveness. However, there is a lack knowledge about how interventions using these strategies could motivate or demotivate behaviours. Therefore, this paper explores the mechanism through which Reward and Punishment motivate or demotivate behaviours with respect to their strengths and weaknesses. The results of large-scale exploratory studies (N = 1768) uncover important strengths and weaknesses that could facilitate or hinder the effectiveness of Reward and Punishment at motivating behaviour change. These include their ability to engage users and make behaviour fun, reinforce commitments to goals, and reveal some consequences of bad behaviour. We also compared the perceived effectiveness of reward and punishment quantitatively. [ABSTRACT FROM AUTHOR]

This article reviews Albert Einstein's first published paper, submitted for publication in 1900. At that time, Einstein was 21 and a recent college graduate. His paper uses modeling and least squares to analyze data in support of a scientific proposition. Einstein is shown to be well trained, for his day, in using statistics as a tool in his scientific research. This paper also shows his ability to make trivial arithmetic mistakes and some clumsiness in data recording. A major aim of this article is to help provide a better appreciation of Einstein as an active user of statistical arguments in this and other of his important publications. [ABSTRACT FROM AUTHOR]

This article revisits sequential estimation of the autoregressive parameter β in a first-order autoregressive (AR(1)) model and construction of a sequential confidence region for a parameter vector θ in a first-order threshold autoregressive (TAR(1)) model. To resolve a theoretical conjecture raised in Sriram (1986), we provide a comprehensive numerical study that strongly suggests that theregretin using a sequential estimator of β can be significantlynegativefor many heavy-tailed error distributions and even for normal errors. Secondly, to investigate yet another conjecture about the limiting distribution of a sequential pivotal quantity for θ in a TAR(1) model, we conduct an extensive numerical study that strongly suggests that the sequential confidence region has much better coverage probability than that of a fixed sample counterpart, regardless of whether the θ values are inside or on or near the boundary of the ergodic region of the series. These highlight the usefulness of sequential sampling methods in fitting linear and nonlinear time series models. [ABSTRACT FROM AUTHOR]

Understanding the flow pressure distribution on the blade airfoil of the tidal turbine is of great significance for optimising the energy harvesting performance of the blades. In this paper, a bidirectional type horizontal tidal turbine (BHTT) with special S-shaped blades is proposed, which have a larger pitch diameter ratio provide excellent performance at low oncoming flow velocity by the theoretical, numerical and experimental methods. First, it is verified that the energy harvesting efficiency is basically the same in the case of bidirectional flow, and the S-shaped blade is divided into multiple slice sections, which could quantify the energy harvesting performance of each area of the blade. Then, using the method of mathematical statistics to divide more areas, the probability density shows a skewed distribution. The results show that the energy harvesting performance is less affected by flow velocity fluctuation, and the energy harvesting efficiency could reach 0.25-0.55 when the tip speed ratio is in the range of 0.2-0.5. Furthermore, the slice section method is adopted to make the influence of axial thrust intuitive and clear to study the turbine energy harvesting performance and improve the harvesting efficiency, which could provide a reference for the engineering design of tidal turbines. [ABSTRACT FROM AUTHOR]

The determination of plotting positions on probability graph paper so that the associated weighted least squares estimators of the scale parameter and the percentiles of a continuous distribution have certain properties is discussed. Necessary and sufficient conditions are given for an invariant optimal plot for percentile estimation. Also discussed is the derivation of ordered plotting positions. [ABSTRACT FROM AUTHOR]

The 2022 International Symposium on Nonparametric Statistics was held in Paphos, Cyprus and co-sponsored by the Institute of Mathematical Statistics and the Bernoulli Society of Mathematical Statistics and Probability. The symposium brought together researchers from around the world to discuss recent advances and trends in nonparametric statistics. The conference covered a wide range of topics, including nonparametric estimation, hypothesis testing, adaptive inference, high-dimensional statistical inference, and more. The special issue of the Journal of Nonparametric Statistics contains papers that have undergone a peer review process and cover diverse areas of nonparametric statistics. [Extracted from the article]

This study aimed to determine how watching lecture videos at 1× and 2× speeds affects memory retention in medical students. A posttest-only experimental design was utilized. The participants were 60 Year-1 and Year-2 medical students. The participants were assigned to one of two groups through stratified randomization: Group 1 would watch the video at 1× speed, and Group 2 at 2× speed. Their performance was assessed using a test comprising 20 multiple-choice questions. The test has been applied immediately after watching the video (Immediate test), and, again after one week (Delayed test). Parametric and non-parametric statistical tests were performed. In the Immediate test, the mean score of the 1× speed group was 11.26 ± 4.06, while 2× speed group's mean score was 10.16 ± 2.46. The difference was not significant t(58) = 1.26, p >.05. In the Delayed test, the mean score of 1× speed group was 9.66 ± 3.94, while 2× speed group's mean score was 8.36 ± 2.80. The difference was not significant t(55) = 1.42, p >.05. Watching the video lecture at 2× speed did not impair memory retention in medical students. This may help students to save time in their dense curricula. Practice points Many medical students watch lecture videos at 2× (double) speed to save time. While this is a time-saver, the negative impact on their learning is unclear. This paper describes a randomized trial that measures the learning impact when medical students watch an instructional video at 2× speed and finds that there is no significant negative impact on their learning. [ABSTRACT FROM AUTHOR]

In order to improve the effect of agricultural economic structure optimisation, this paper builds an agricultural economic structure optimisation analysis system based on factor analysis and intelligent algorithms, and uses a set of low-dimensional hidden factor vectors to describe the covariance matrix structure of high-dimensional observation vectors. Moreover, this paper combines the algorithm with the actual situation to obtain the optimisation analysis process of the agricultural economic structure. On this basis, this paper analyses the optimisation of agricultural economic structure in practice with a case analysis method. Moreover, this paper uses mathematical analysis to process agricultural economic structure data, and uses mathematical statistics to visualise the process of data processing. In addition, this paper combines the weighted average to perform parameter processing, combines with the comparative analysis method to obtain the agricultural economic results parameters, and analyses these parameters. Finally, on the basis of the above, this paper proposes the corresponding optimisation strategy of agricultural economic structure. The research results show that the method proposed in this paper has a certain effect. [ABSTRACT FROM AUTHOR]

Maximum likelihood estimators have enormous computational problems. Modified maximum likelihood estimators have no such problems and are equally efficient. The correct authorship of these estimators is pointed out and their numerous applications mentioned. [ABSTRACT FROM AUTHOR]

Maji et al. [Robust statistical inference based on the C-divergence family. Ann Inst Stat Math. 2019;71:1289–1322] introduced the minimum C-divergence estimators and plugging them in the C-divergence measures give test statistics for testing simple null and composite null hypotheses. One inconvenience of these test statistics is that their asymptotic distribution is not, in general, a chi-square distribution but a linear combination of chi-square distributions. To overcome this inconvenience, in this paper we consider Wald-type test statistics based on minimum C-divergence estimators. We establish that this family of test statistics is a chi-square distribution and we get an approximation of the power function under simple null hypothesis and composite null hypothesis. We have calculated both first order and second order influence function of the Wald-type test statistics and based on it we can see the robustness of the family of test statistics considered in this paper. Both simulated and real data examples have been shown as part of numerical results. [ABSTRACT FROM AUTHOR]

Effective teaching of concepts related to human computer interaction (HCI) requires introduction of the core paradigms as well as the design and evaluation methodologies to the learners. In this paper, we investigate the learning effectiveness of a tool-mediated learning activity to support instruction of established human performance models, namely the Keystroke Level Model (KLM) and Fitts' law, and their application in web form design practice. The tool, named Keystroke Level Model Form Analyser (KLM-FA), supports learning through exploration by providing step-by-step tracing of the KLM modelling for any web form filling task. KLM-FA can be used in modelling exercises of either online or offline web forms according to different interaction strategies or users' characteristics. Three pretest-posttest studies involving 52 students in total enrolled in computer science curricula with different education delivery methods (campus-based, blended learning, distance learning) and levels (undergraduate, postgraduate) provide evidence for the effectiveness of the proposed learning activity. In all three studies, it was found that the KLM-FA activity had a significant positive effect on students' learning gain. In addition, students rated their perceived educational experience and KLM-FA usability as rather high. Content analysis of students' comments also found that KLM-FA is an educationally valuable and usable tool. [ABSTRACT FROM AUTHOR]

Take a family of independent events. If some of these events, or all of them, are replaced by their complements, then independence still holds. This fact, which is agreed upon by the members of the statistical/probability communities, is tremendously well known, is fairly intuitive and has always been frequently used for easing probability calculations and allowing important developments in probability theory. However, can this result be proven without advanced elements from probability theory, such as independent σ-fields and related results? This paper aims primarily to fill this possible gap. Two elementary proofs that require only introductory probability content are given in detail and compared with the 'technical' proof found in books on advanced probability theory. A discussion regarding how these proofs could be included in regular probability courses is also included in the survey. [ABSTRACT FROM AUTHOR]

The paper by Johnson [Systems of frequency curves generated by the methods of translation, Biometrika 36 (2014), pp. 149-176] has introduced a very interesting univariate distribution with bounded support which is known in the statistical literature as the class of distributions. In this paper we generalize this class of univariate distributions to the multivariate case whose marginals are distributions. On the basis of the multivariate distribution introduced, we propose a multivariate regression model for dealing with multivariate response variables which are vectors of rates or proportions. We consider a frequentist approach to perform inferences, and the maximum likelihood method is employed to estimate the model parameters. Monte Carlo simulation results reveal that the maximum likelihood method can be used effectively in estimating the model parameters. An application to real data is presented to show the usefulness of the multivariate regression model in practice. [ABSTRACT FROM AUTHOR]

The article discusses on an article by David R. Bellhouse published within "Historia Mathematica" in its May 2007 issue. The article by Bellhouse discusses on the work of Philip Stanhope, the second earl of Stanhope, on probability theory and his correspondence with Bishop Berkeley's criticism on Isaac Newton's calculus. Bellhouse writes that Stanhope was strongly influenced by Abraham de Moivre's work on a method of calculating the probability of events in play and by Pierre Rémond's essay. Bellhouse adds that one of Stanhope's contribution to mathematics was his work on determining the probability of a run of at least r sucesses in n trials which was posed by de Moivre. Stanhope also worked on the duration of play in the gambler's ruin problem.

The purpose of this paper is to propose a revision of the well-known Campbellian system for causal research. The revised system, termed the COPS model, applies to both applied and basic research. Five validities are included, where two validities are adopted from the Campbellian system, and the validities are partly hierarchically ordered. Important similarities and differences between the Campbellian system and the COPS model are discussed. [ABSTRACT FROM AUTHOR]

Application of the exact statistical inference frequently leads to non-standard probability distributions of the considered estimators or test statistics. The exact distributions of many estimators and test statistics can be specified by their characteristic functions, as is the case for the null distribution of the Bartlett's test statistic. However, analytical inversion of the characteristic function, if possible, frequently leads to complicated expressions for computing the distribution function and the corresponding quantiles. An efficient alternative is the well-known method based on numerical inversion of the characteristic functions, which is, however, ignored in popular statistical software packages. In this paper, we present the explicit characteristic function of the corrected Bartlett's test statistic together with the computationally fast and efficient implementation of the approach based on numerical inversion of this characteristic function, suggested for evaluating the exact null distribution used for testing homogeneity of variances in several normal populations, with possibly unequal sample sizes. [ABSTRACT FROM AUTHOR]

Standard meta-analysis requires the quantity of interest and its estimated variance to be reported for each study. Datasets that lack such variance information pose important challenges to meta-analytic inference. In a study with continuous outcomes, only sample means and sample sizes may be reported in the treatment arm. Classical meta-analytical technique is unable to apply statistical inference to such datasets. In this paper, we propose a statistical tool for testing equal means between two groups in meta-analysis when the variances of the constituent studies are unreported, using pivot inference based on the exact t-distribution and the generalized likelihood ratio. These are considered under a fixed-effect model. In simulations, the type I errors and power probabilities of the proposed tests are investigated as metrics of their performance. The t-test statistic provides type I errors very close to the nominal significance level in all cases and has large power. The generalized likelihood ratio test statistic performs well when the number of studies is moderate-to-large. The performance of our tests surpasses that of the conventional test, which is based on the normal distribution. The difference is especially pronounced when the number of studies is small. The distribution given by our tests is also shown to closely follow the theoretical distribution. [ABSTRACT FROM AUTHOR]

The paper presents the analysis of speech perception and of the specific nature of communication between migrants and residents of Moscow, as reflected in the digital environment. The main focus is on conflictogenic digital zones, as well as methods for predicting and preventing conflicts. The development of algorithms to make predictions about users' possible actions, the occurrence and prevention of conflicts is an important task of interdisciplinary research. The goals of research were achieved based on the analysis of social media data. Neural network modeling, statistical analysis, and differential equations were used as research methods. In mathematical modeling, three types of models were built: an equation of linear regression, as well as logistic and type-epidemiological mathematical models. The study showed that the use of parallel models using differential equations, mathematical statistics and neural network technology to determine the dynamics of aggressive online activity, in particular, to analyze users' perception of conflict situations related to the topic of migrants, makes it possible to correctly analyze conflict zones in the development of a modern metropolis, to increase the effectiveness of research methods and predictive analytics of the development of social tension. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of making statistical inference for a truncated normal distribution under progressive type I interval censoring. We obtain maximum likelihood estimators of unknown parameters using the expectation-maximization algorithm and in sequel, we also compute corresponding midpoint estimates of parameters. Estimation based on the probability plot method is also considered. Asymptotic confidence intervals of unknown parameters are constructed based on the observed Fisher information matrix. We obtain Bayes estimators of parameters with respect to informative and non-informative prior distributions under squared error and linex loss functions. We compute these estimates using the importance sampling procedure. The highest posterior density intervals of unknown parameters are constructed as well. We present a Monte Carlo simulation study to compare the performance of proposed point and interval estimators. Analysis of a real data set is also performed for illustration purposes. Finally, inspection times and optimal censoring plans based on the expected Fisher information matrix are discussed. [ABSTRACT FROM AUTHOR]

Markov kernels play a decisive role in probability and mathematical statistics theories, and are an extension of the concepts of σ -field and statistic. Concepts such as independence, sufficiency, completeness, ancillarity or conditional distribution have been extended previously to Markov kernels. In this paper, the concept of conditional expectation of a Markov kernel given another is introduced, setting its first properties. An application to clinical diagnosis is provided, obtaining an optimality property of the predictive values of a diagnosis test. In a statistical framework, this new probabilistic tool is used to extend to Markov kernels the theorems of Rao-Blackwell and Lehmann-Scheffé. A result about the completeness of a sufficient statistic is obtained in passing by properly enlarging the family of probabilities. As a final statistical scholium, a generalization of a result about the completeness of the family of nonrandomized estimators is given. [ABSTRACT FROM AUTHOR]

In this paper, we consider the drift parameters estimation problem for the Vasicek-type model defined as d X t = a (b − X t) d t + d G t , X 0 = 0 , t ≥ 0 where a < 0 and b ∈ R are considered as unknown drift parameters and Gt is a self-similar Gaussian process with index L ∈ (1 / 2 , 1) . We provide sufficient conditions, based on the properties of G, ensuring the strong consistency and the asymptotic distributions of our estimators a ̂ of a and b ̂ of b based on the observation { X t } t ∈ [ 0 , T ] as T → ∞ . Our approach extend the result of Xiao and Yu (2017) for the case when G is a fractional Brownian motion with Hurst parameter H ∈ (1 2 , 1) . We also discuss the cases of sub-fractional Browian motion and bi-fractional Brownian motion. The conclusion can also be extended to more general self-similarity processes, such as Hermite processes. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to prove a weak convergence result for empirical processes indexed in general classes of functions and with an underlying α-mixing triangular array of random variables. In particular, the uniformly boundedness assumption on the function class, which is required in most of the existing literature, is spared. Furthermore, under strict stationarity a weak convergence result for the sequential empirical process indexed in function classes is obtained as a direct consequence. Two examples in mathematical statistics, that cannot be treated with existing results, are given as possible applications. [ABSTRACT FROM AUTHOR]

It is desirable to work efficiently and cost effectively to evaluate new therapies in a time-sensitive and ethical manner without compromising the integrity and validity of the development process. The seamless phase II/III clinical trial has been proposed to meet this need, and its efficient, ethical and economic advantages can be strengthened by its combination with innovative response adaptive randomization (RAR) procedures. In particular, well-designed frequentist RAR procedures can target theoretically optimal allocation proportions, and there are explicit asymptotic results. However, there has been little research into seamless phase II/III clinical trials with frequentist RAR because of the difficulty in performing valid statistical inference and controlling the type I error rate. In this paper, we propose the framework for a family of frequentist RAR designs for seamless phase II/III trials, derive the asymptotic distribution of the parameter estimators using martingale processes and offer solutions to control the type I error rate. The numerical studies demonstrate our theoretical findings and the advantages of the proposed methods. [ABSTRACT FROM AUTHOR]

Consider a repairable system subject to shocks that arrive according to a non-homogeneous Poisson process (NHPP). As a shock occurs, two types of failure may be happened. Type-I failure occurs with probability q and is rectified by a minimal repair, whereas type-II failure takes place with probability p = 1−q and is removed by replacement. The system is replaced at the nth type I failure or at type II failure, whichever comes first. In the present paper, we find a general representation for the likelihood function of the proposed model. Then, we follow both classical and Bayesian procedures to estimate the model parameters when the time to first failure is a Weibull distribution. Because the Bayesian estimation cannot be obtained in a closed form, we use two approximation methods: Lindley's approximation and MCMC method. Finally, a Monte Carlo simulation is conducted to compare the performance of estimators in classical and Bayesian procedures. [ABSTRACT FROM AUTHOR]

This paper proposes a new generator function based on the inverted Kumaraswamy distribution and introduces 'generalized inverted Kumaraswamy-G' family of distributions. We provide a comprehensive account of some of its mathematical properties that include the ordinary and incomplete moments, quantile and generating functions and order statistics. The infinite mixture representations for probability density and cumulative distribution and entropy functions of the new family are also established. The density function of the ith-order statistics is expressed as an infinite linear combination of baseline densities and model parameters are estimated by maximum likelihood method. Four special models of this family are also derived along with their respective hazard rate functions. The maximum likelihood estimation (MLE) method is used to obtain the model parameters. Monte Carlo simulation experiments are executed to assess the performance of the ML estimators under the corresponding generated models while some data applications are also illustrated. The results of the study show that the proposed distribution is more flexible as compared to the baseline model. This distribution especially can be used to model symmetric, left-skewed, right-skewed and reversed-J data sets. [ABSTRACT FROM AUTHOR]

The purpose of this paper is twofold. First, we investigate estimations in varying-coefficient partially linear errors-in-variables models with covariates missing at random. However, the estimators are often biased due to the existence of measurement errors, the bias-corrected profile least-squares estimator and local liner estimators for unknown parametric and coefficient functions are obtained based on inverse probability weighted method. The asymptotic properties of the proposed estimators both for the parameter and nonparametric parts are established. Second, we study asymptotic distributions of an empirical log-likelihood ratio statistic and maximum empirical likelihood estimator for the unknown parameter. Based on this, more accurate confidence regions of the unknown parameter can be constructed. The methods are examined through simulation studies and illustrated by a real data analysis. [ABSTRACT FROM AUTHOR]

The estimation of variance function plays an extremely important role in statistical inference of the regression models. In this paper we propose a variance modelling method for constructing the variance structure via combining the exponential polynomial modelling method and the kernel smoothing technique. A simple estimation method for the parameters in heteroscedastic linear regression models is developed when the covariance matrix is unknown diagonal and the variance function is a positive function of the mean. The consistency and asymptotic normality of the resulting estimators are established under some mild assumptions. In particular, a simple version of bootstrap test is adapted to test misspecification of the variance function. Some Monte Carlo simulation studies are carried out to examine the finite sample performance of the proposed methods. Finally, the methodologies are illustrated by the ozone concentration dataset. [ABSTRACT FROM AUTHOR]

The generalized case-cohort design is widely used in large cohort studies to reduce the cost and improve the efficiency. Taking prior information of parameters into consideration in modeling process can further raise the inference efficiency. In this paper, we consider fitting proportional hazards model with constraints for generalized case-cohort studies. We establish a working likelihood function for the estimation of model parameters. The asymptotic properties of the proposed estimator are derived via the Karush-Kuhn-Tucker conditions, and their finite properties are assessed by simulation studies. A modified minorization-maximization algorithm is developed for the numerical calculation of the constrained estimator. An application to a Wilms tumor study demonstrates the utility of the proposed method in practice. [ABSTRACT FROM AUTHOR]

The aim of this paper is to develop the estimation procedures for the reliability functions R(t) and P, when the available data have the form of progressively type-II right censored sample. It is supposed that X-sample and X*-sample are independent and generated from the two different proportional hazard rate models, respectively, with different probability parameters which covers many lifetime distributions as specific cases [see Basirat M, Baratpour S, Jafar A. Statistical inferences for the proportional hazard models based on progressive type-II censored samples. J Stat Comput Simul. 2014. Available from: ]. Point estimation (classical as well as Bayesian) procedures and asymptotic confidence intervals are developed for parameter α, and. Testing procedures are also developed for the hypotheses related to various parametric functions. The performances of these estimators are studied by using Monte Carlo simulation technique. Finally, the use of the proposed estimators is shown in an illustrative example. [ABSTRACT FROM AUTHOR]

Much research has been conducted over the last half century in developing stochastic processes, and their dynamical nature. Typically, for time indexed processes, the temporal distribution is restricted to those having marginal distributions of a specified and familiar lifetime family. Extensions of temporal models to the spatio-temporal setting can be challenging. We generalize the results from a spatial statistic that captures local correlation, Moran's index, to the spatio-temporal frame and describe a model that can be applied to temporal dynamical phenomena. The proposed approach leads to novel statistical inference results. Ensuring a foundational Moran measure is critical in describing event occurrence and progression over time of the process from observed initial conditions. In this paper, we provide a descriptive form of discrete spatio-temporal Moran's index statistics based on processes motivated by the spread of an infectious plant disease in an agricultural setting. This family possesses an underlying Poisson point process in space and time. Estimators are developed and applied to simulated data and the output are analyzed. Our results adds substantially to known results in the literature and elude to the description of the time dependent Moran's values. [ABSTRACT FROM AUTHOR]

There are several failure modes may cause system failed in reliability and survival analysis. It is usually assumed that the causes of failure modes are independent each other, though this assumption does not always hold. Dependent competing risks modes from Marshall-Olkin bivariate Weibull distribution under Type-I progressive interval censoring scheme are considered in this paper. We derive the maximum likelihood function, the maximum likelihood estimates, the 95% Bootstrap confidence intervals and the 95% coverage percentages of the parameters when shape parameter is known, and EM algorithm is applied when shape parameter is unknown. The Monte-Carlo simulation is given to illustrate the theoretical analysis and the effects of parameters estimates under different sample sizes. Finally, a data set has been analyzed for illustrative purposes. [ABSTRACT FROM AUTHOR]

In this paper, a new compound continuous distribution named the Gompertz Fréchet distribution which extends the Frèchet distribution was developed. Its various statistical properties were also derived and estimation of model parameters was considered using the maximum likelihood estimation method. The application of the Gompertz Fréchet distribution was provided using real-life data sets and its performance was compared with Gompertz Weibull distribution, Gompertz Lomax distribution and Gompertz Burr XII distribution. [ABSTRACT FROM AUTHOR]

This paper is devoted to the estimation of the derivative of the regression function in fixed-design nonparametric regression. We establish the almost sure convergence as well as the asymptotic normality of our estimate. We also provide concentration inequalities which are useful for small sample sizes. Numerical experiments on simulated data show that our nonparametric statistical procedure performs very well. We also illustrate our approach on high-frequency environmental data for the study of marine pollution. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the progress of variant of conceptual predictive () statistic and we propose the model selection criterion that depend on statistic under ridge regression for linear mixed model selection. The proposed criterion is conditional ridge () statistic based on the expected conditional Gauss discrepancy. Two versions of statistic under the assumptions that the variance components are known and unknown are derived. To examine the performance of the proposed criterion, a real data analysis and a Monte Carlo simulation study are given. [ABSTRACT FROM AUTHOR]

Periodic autoregressive (PAR) models with symmetric innovations are widely used on time series analysis, whereas its asymmetric counterpart inference remains a challenge, because of a number of problems related to the existing computational methods. In this paper, we use an interesting relationship between periodic autoregressive and vector autoregressive (VAR) models to study maximum likelihood and Bayesian approaches to the inference of a PAR model with normal and skew-normal innovations, where different kinds of estimation methods for the unknown parameters are examined. Several technical difficulties which are usually complicated to handle are reported. Results are compared with the existing classical solutions and the practical implementations of the proposed algorithms are illustrated via comprehensive simulation studies. The methods developed in the study are applied and illustrate a real-time series. The Bayes factor is also used to compare the multivariate normal model versus the multivariate skew-normal model. [ABSTRACT FROM AUTHOR]

In this paper, we consider a measure of inaccuracy between distributions of the nth record value and parent random variable. We also propose the measure of residual inaccuracy of record values and study characterization results of dynamic cumulative residual inaccuracy measure. We discuss some properties of the proposed measures. [ABSTRACT FROM AUTHOR]

A skipped correlation has the advantage of dealing with outliers in a manner that takes into account the overall structure of the data cloud. For p-variate data, p ≥ 2, there is an extant method for testing the hypothesis of a zero correlation for each pair of variables that is designed to control the probability of one or more Type I errors. And there are methods for the related situation where the focus is on the association between a dependent variable and p explanatory variables. However, there are limitations and several concerns with extant techniques. The paper describes alternative approaches that deal with these issues. [ABSTRACT FROM AUTHOR]

In many problems involving generalized linear models, the covariates are subject to measurement error. When the number of covariates p exceeds the sample size n, regularized methods like the lasso or Dantzig selector are required. Several recent papers have studied methods which correct for measurement error in the lasso or Dantzig selector for linear models in the p > n setting. We study a correction for generalized linear models, based on Rosenbaum and Tsybakov's matrix uncertainty selector. By not requiring an estimate of the measurement error covariance matrix, this generalized matrix uncertainty selector has a great practical advantage in problems involving high-dimensional data. We further derive an alternative method based on the lasso, and develop efficient algorithms for both methods. In our simulation studies of logistic and Poisson regression with measurement error, the proposed methods outperform the standard lasso and Dantzig selector with respect to covariate selection, by reducing the number of false positives considerably. We also consider classification of patients on the basis of gene expression data with noisy measurements. Supplementary materials for this article are available online. [ABSTRACT FROM AUTHOR]

In this paper, some complete convergence and complete moment convergence results for arrays of rowwise negatively superadditive dependent (NSD, in short) random variables are studied. The obtained theorems not only extend the result of Gan and Chen (2007) to the case of NSD random variables, but also improve them. [ABSTRACT FROM AUTHOR]

This paper is concerned with the conditional feature screening for ultra-high dimensional right censored data with some previously identified important predictors. A new model-free conditional feature screening approach, conditional correlation rank sure independence screening, has been proposed and investigated theoretically. The suggested conditional screening procedure has several desirable merits. First, it is model free, and thus robust to model misspecification. Second, it has the advantage of robustness of heavy-tailed distributions of the response and the presence of potential outliers in response. Third, it is naturally applicable to complete data when there is no censoring. Through simulation studies, we demonstrate that the proposed approach outperforms the CoxCS of Hong et al. under some circumstances. A real dataset is used to illustrate the usefulness of the proposed conditional screening method. [ABSTRACT FROM AUTHOR]

In this paper, some of the properties of non parametric estimation of the expectation ofg(X) (any function ofX), by using a judgment poststratification sample (JPS), have been discussed. A class of estimators (including the standard JPS estimator and a JPS estimator proposed by Frey and Feeman (2012, Comput. Stat. Data An.) is considered. The paper provides mean and variance of the members of this class, and examines their consistency and asymptotic distribution. Specifically, the results are for the estimation of population mean, population variance, and cumulative distribution function. We show that any estimators of the class may be less efficient than simple random sampling (SRS) estimator for small sample sizes. We prove that the relative efficiency of some estimators in the class with respect to balanced ranked set sampling (BRSS) estimator tends to 1 as the sample size goes to infinity. Furthermore, the standard JPS mean estimator, and Frey–Feeman JPS mean estimator are specifically studied and we show that two estimators have the same asymptotic distribution. For the standard JPS mean estimator, in perfect ranking situations, optimum values ofH(the ranking class size), for different sample sizes, are determined non parametrically for populations that are not heavily skewed or thick tailed. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the following simple linear errors-in-variables regression model:where θ and β are the unknown parameters, ηi, ξi’s are observable andxi’s are unobservable. We assume the error variables {(ε1, δi), 1≤i≤n} form aL2stationary α-mixing sequences. In this paper, we obtained the moderate deviation principles for the least-square estimators of the unknown parameters θ and β. [ABSTRACT FROM AUTHOR]

The score statisticS2is commonly used for general likelihood-based inference. Pearson’s Chi-squared statisticX2= ∑(O−E)2/Eis ubiquitous in contingency table inference. Because tests and confidence intervals based onS2have been shown to work well in practice and theory and becauseX2has such a simple and intuitively appealing form, it is of interest to know whenS2is identical toX2and whenX2has an approximate Chi-squared distribution. Toward these ends, this paper gives a simple proof thatS2=X2for 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. [ABSTRACT FROM AUTHOR]

Traditional outlier detection methods such as the minimum volume ellipsoid method and MCD method are all based on normal distance. As is well known, the norm-based distance is only effective in detecting difference with dense signals. However, these existing approaches will encounter detection power loss under the sparse signals settings. In this paper, we try to solve the problem of detecting outliers under the sparsity assumption by adapting the thresholding method. The proposed outlier detection procedure finds the clean set by the minimum diagonal product algorithm, then the maximum thresholding statistic is employed to identify the outlier. The finite sample performance of our method is evaluated through simulations. Compared with the existing outlier detection methods, simulation results show that our proposed outlier detection procedure is very efficient under sparse settings. [ABSTRACT FROM AUTHOR]

Analysis of means (ANOM) is a powerful tool for comparing means and variances in fixed-effects models. The graphical exhibit of ANOM is considered as a great advantage because of its interpretability and its ability to evaluate the practical significance of the mean effects. However, the presence of random factors may be problematic for the ANOM method. In this paper, we propose an ANOM approach that can be applied to test random effects in many different balanced statistical models including fixed-, random- and mixed-effects models. The proposed approach utilizes the range of the treatment averages for identifying the dispersions of the underlying populations. The power performance of the proposed procedure is compared to the analysis of variance (ANOVA) approach in a wide range of situations via a Monte Carlo simulation study. Illustrative examples are used to demonstrate the usefulness of the proposed approach and its graphical exhibits, provide meaningful interpretations, and discuss the statistical and practical significance of factor effects. [ABSTRACT FROM AUTHOR]

In this paper we introduce a new method for detecting outliers in a set of proportions. It is based on the construction of a suitable twoway contingency table and on the application of an algorithm for the detection of outlying cells in such table. We exploit the special structure of the relevant contingency table to increase the efficiency of the method. The main properties of our algorithm, together with a guide for the choice of the parameters, are investigated through simulations, and in simple cases some theoretical justifications are provided. Several examples on synthetic data and an example based on pseudo-real data from biological experiments demonstrate the good performances of our algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we mainly study the complete moment convergence of double-indexed randomly weighted sums of negatively superadditive-dependent (NSD, for short) random variables, which is stronger than complete convergence. In addition, the convergence of double-indexed randomly weighted sums of NSD random variables is also obtained. As applications, we obtain the complete consistency for the randomly weighted estimator in a nonparametric regression model based on NSD errors, and study the almost sure convergence and mean square convergence of the state observers of linear-time-invariant systems. [ABSTRACT FROM AUTHOR]

To estimate the central tendency or location of a sample of interval-valued data, a standard statistic is the interval-valued sample mean. Its strong sensitivity to outliers or data changes motivates the search for more robust alternatives. In this respect, a more robust location statistic is studied in this paper. This measure is inspired by the concept of spatial median and makes use of the versatile generalized Bertoluzza's metric between intervals, the so-called distance. The problem of minimizing the mean distance to the values the random interval takes, which defines the spatial-type -median, is analysed. Existence and uniqueness of the sample version are shown. Furthermore, the robustness of this proposal is investigated by deriving its finite sample breakdown point. Finally, a real-life example from the Economics field illustrates the robustness of the sample -median, and simulation studies show some comparisons with respect to the mean and several recently introduced robust location measures for interval-valued data. [ABSTRACT FROM AUTHOR]

In this paper we study the problem of statistical inference on the parameters of the semiparametric variance-mean mixtures. This class of mixtures has recently become rather popular in statistical and financial modelling. We design a semiparametric estimation procedure that first estimates the mean of the underlying normal distribution and then recovers non-parametrically the density of the corresponding mixing distribution. We illustrate the performance of our procedure on simulated and real data. [ABSTRACT FROM AUTHOR]