Search

The purpose of this note is to point out a problem related to stress-strength models in some published papers. This difficulty has occurred in the asymptotic variance of the maximum likelihood estimator of the stress-strength parameter. The asymptotic variance will be studied in general and then in the mentioned papers. Finally, the correct version of asymptotic variance is computed. [ABSTRACT FROM AUTHOR]

The change point estimation concept is usually useful in time series models. This concept helps to decrease the decision making or production costs by monitoring the stock market and production lines. It is also applied in several fields such as Financing and Quality Control. In this paper, it is assumed that the ARMA (1) model exists between the sample statistics of x ¯ control chart. A maximum likelihood technique is developed to estimate the change point at which the stationary ARMA (1) model changes into a non-stationary process. For the estimation of unknown parameters after the change point, the Smoothing of Dynamic Linear Model has been used based on singular value decomposition. It is assumed that there exists a correlation between sample statistics. Simulation results show the effectiveness of the estimators proposed in this paper to estimate the change point of the stationary state in ARMA (1) model. An example is provided to illustrate the application. [ABSTRACT FROM AUTHOR]

In this paper a new family of Harris skewed normal distributions (HSND) is proposed. The probability density function of the HSND can be both positively and negatively skewed, unimodal and multimodal and can be symmetric with heavy tails. Monte Carlo simulations are conducted to evaluate the applicability of the proposed family of distributions. The HSND family is used to fit three different real data sets. [ABSTRACT FROM AUTHOR]

In this paper, two-parameter Poisson binomial-exponential 2 (PBE2) distribution is firstly reviewed, then a new integer-valued autoregressive (INAR) model with PBE2 innovations is proposed. The definition and statistical properties of the proposed model are given, including the mean, variance, covariance, strict stationarity and ergodicity. Two-step conditional least squares and conditional maximum likelihood estimation methods are considered to estimate the parameters. To assess the proposed model, a crime data set is analyzed and a comparison with other competing INAR models is given, which shows that the proposed model yields a better performance. [ABSTRACT FROM AUTHOR]

The edges in networks are not only binary, either present or absent, but also take weighted values in many scenarios (e.g., the number of emails between two users). The covariate-p0 model has been proposed to model binary directed networks with the degree heterogeneity and covariates. However, it may cause information loss when it is applied in weighted networks. In this paper, we propose to use the Poisson distribution to model weighted directed networks, which admits the sparsity of networks, the degree heterogeneity and the homophily caused by covariates of nodes. We call it the network Poisson model. The model contains a density parameter μ, a 2n-dimensional node parameter θ and a fixed dimensional regression coefficient γ of covariates. Since the number of parameters increases with n, asymptotic theory is non standard. When the number n of nodes goes to infinity, we establish the ℓ ∞ -errors for the maximum likelihood estimators (MLEs), θ ̂ and γ ̂ , which are O p ( ( log n / n) 1 / 2) for θ ̂ and O p ( log n / n) for γ ̂ , up to an additional factor. We also obtain the asymptotic normality of the MLE. Numerical studies and a data analysis demonstrate our theoretical findings. [ABSTRACT FROM AUTHOR]

The usefulness of a hidden truncated Pareto (type II) model along with its' inference under both the classical and Bayesian paradigm have been discussed in the literature in great details. In the multivariate set-up, some discussions are made that are primarily based on constructing a multivariate hidden truncated Pareto (type II) models with — single variable truncation or more than one variable truncation. However, in all such previous discussions regarding bivariate hidden truncated Pareto models, in the classical estimation set-up, large bias and standard error values for the truncation parameter(s) as well as for the other parameters have been observed, and no discussion was made to address this issue. In this article, we try to address this issue of large bias values by considering constrained optimization via linear/non-linear transformation of the parameters following the strategy as proposed (the reference is given in Section 3), in efficiently implementing Newton-Raphson optimization algorithm in R. This plays a major motivation for the present paper. We also derive the observed Fisher Information Matrix. For illustrative purposes, we provide a simulation study to address this issue. A real-life data set is also re-analyzed to study the utility of such two-sided hidden truncation Pareto (type II) models. [ABSTRACT FROM AUTHOR]

In cluster-specific studies, ordinary logistic regression and conditional logistic regression for binary outcomes provide maximum likelihood estimator (MLE) and conditional maximum likelihood estimator (CMLE), respectively. In this paper, we show that CMLE is approaching to MLE asymptotically when each individual data point is replicated infinitely many times. Our theoretical derivation is based on the observation that a term appearing in the conditional average log-likelihood function is the coefficient of a polynomial, and hence can be transformed to a complex integral by Cauchy's differentiation formula. The asymptotic analysis of the complex integral can then be performed using the classical method of steepest descent. Our result implies that CMLE can be biased if individual weights are multiplied with a constant, and that we should be cautious when assigning weights to cluster-specific studies. [ABSTRACT FROM AUTHOR]

Grouped and right-censored (GRC) count data are widely adopted to study some sensitive topics or to collect information from less cognitive respondents in many research fields, such as psychology, sociology, and criminology. However, theoretical analysis of GRC counts is involved due to the co-existence of grouping schemes and right-censoring schemes. Recently, a modified Poisson regression model has been proposed to analyze GRC count data under the framework of maximum likelihood estimation. In this paper, I study the asymptotic properties of the maximum likelihood estimators of GRC counts that can cover the modified Poisson estimator. Existing results on modified Poisson estimators for GRC counts are only applicable to stochastic regressors with strictly positive definite Fisher information matrices. Results in this paper are derived under a milder condition that the information matrix of observations is divergent, which can cover the results for the stochastic case in the almost sure sense. Real data simulations are provided to investigate drug use in America. [ABSTRACT FROM AUTHOR]

Estimation of causal treatment effects has attracted a great deal of interest in many areas including social, biological and health science, and for this, instrumental variable (IV) has become a commonly used tool in the presence of unmeasured confounding. In particular, many IV methods have been developed for right-censored time-to-event outcomes. In this paper, we consider a much more complicated situation where one faces interval-censored time-to-event outcomes, which are ubiquitously present in studies with, for example, intermittent follow-up but are challenging to handle in terms of both theory and computation. A sieve maximum likelihood estimation procedure is proposed for estimating complier causal treatment effects under the additive hazards model, and the resulting estimators are shown to be consistent and asymptotically normal. A simulation study is conducted to evaluate the finite sample performance of the proposed approach and suggests that it works well in practice. It is applied to a breast cancer screening study. [ABSTRACT FROM AUTHOR]

In this paper, the longitudinal data analysis is used to interpret the balanced Bühlmann credibility model with correlation risk, and the homogeneous credibility estimator is derived. We obtain the restricted maximum likelihood estimators (RMLE) for the structural parameters involved in the credibility factor and show that they are unbiased. In addition, the linear Bayes method is employed to estimate the structural parameters, and the proposed linear Bayes estimators (LBE) appear to outperform RMLE in terms of the mean squared error matrix (MSEM) criterion. Simulation studies show that the proposed LBE performs well. [ABSTRACT FROM AUTHOR]

The random coefficient autoregressive (RCAR) processes are very useful to model time series in applications. It is commonly observed that the random autoregressive coefficient is assumed to be an independent identically distributed (i.i.d.) random variable sequence. To make the RCAR model more practical, this paper considers a new RCAR(1) model driven by explanatory variable and observations. We use the conditional least squares, the quantile regression and the conditional maximum likelihood methods to estimate the model parameters. The consistency and asymptotic normality of the proposed estimates are established. Simulation studies are conducted for the evaluation of the developed approaches and two applications to real-data examples are provided. The results show that the proposed procedures perform well for the simulations and application. [ABSTRACT FROM AUTHOR]

This paper considers the parameter estimation for the inverse Gaussian regression model (IGRM) in the presence of multicollinearity. The inverse Gaussian modified ridge-type estimator (IGMRTE) is developed for efficient parameter estimation and compared with other estimation methods such as the maximum likelihood estimator (MLE), ridge and Liu estimator. We derived the properties of the proposed estimator and conducted a theoretical comparison with some of the existing estimators using the matrix mean squared error and mean squared error criterions. Furthermore, the statistical properties of these estimators are systematically scrutinized via a Monte Carlo simulation study under different conditions. The findings of the simulation study demonstrate that the proposed IGMRTE showed a much more robust behavior in the presence of severe multicollinearity. A real life example is also analyzed to evaluate the effectiveness of the estimators under study. Both the simulation and the application results confirm the use of IGMRTE for the estimation of unknown regression coefficients of the IGRM when the explanatory variables are highly correlated. [ABSTRACT FROM AUTHOR]

The polychoric correlation is a parametric measure of the correlation between two unobserved continuous variables when the observed variables are discrete. In this paper we propose a robust version of the polychoric correlation. Robust polychoric correlation is shown to be consistent and asymptotically normal. Results from a systematic Monte Carlo simulation suggest that the new estimator has better robustness properties than normality based maximum likelihood estimation of the polychoric correlation, with negligible costs to efficiency. [ABSTRACT FROM AUTHOR]

The aim of the paper is to determine maximum-likelihood estimation equations. Observations follow a multivariate normal distribution,, where,anddescribe the unknown covariance structure between rows and columns of, respectively. Imposing restrictions onandfour types of covariance structures will be considered. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of efficient estimation for the drift parameter θ ∈ R d in the linear model Z t : = θ t + σ 1 B H 1 (t) + σ 2 B H 2 (t) , t ∈ [ 0 , T ]. Where B H 1 and B H 2 are two independent d-dimensional fractional Brownian motions with Hurst indices H1 and H2 such that 1 2 ≤ H 1 < H 2 < 1. The main goal is firstly to define the maximum likelihood estimator (MLE) of the drift θ, and secondly to provide a sufficient condition for the James-Stein type estimators which dominate, under the usual quadratic risk, the usual estimator (MLE). [ABSTRACT FROM AUTHOR]

In this paper, we discuss some theoretical results and properties of a discrete version of the Birnbaum-Saunders distribution. We present a proof of the unimodality of this model. Moreover, results on moments, quantile function, reliability and order statistics are also presented. In addition, we propose a regression model based on the discrete Birnbaum-Saunders distribution. The model parameters are estimated by the maximum likelihood method and a Monte Carlo study is performed to evaluate the performance of the estimators. Finally, we illustrate the proposed methodology with the use of real data sets. [ABSTRACT FROM AUTHOR]

This paper is an effort to obtain the point estimators and interval estimators for the unknown parameters, reliability and hazard rate functions of bathtub-shaped distribution based on generalized progressive hybrid censoring. We first derive the maximum likelihood estimators for the quantities and compute the estimates using Newton iterative method. Observed Fisher's information matrix is obtained and then the asymptotic confidence intervals are constructed. Besides, two bootstrap confidence intervals are proposed for the quantities. The Bayesian estimators are acquired under squared error loss function using Lindley method and Metropolis-Hastings method with Gibbs sampling, and Bayesian credible intervals are constructed based on Markov Chain Monte Carlo (MCMC) samples as well. Finally, extensive simulation studies are conducted to compare the performance of the estimators and a real data set is analyzed for illustrative purpose. [ABSTRACT FROM AUTHOR]

In the context of reliability theory, Eginhard J. Muth introduced in 1977 a continuous probability distribution that has been overlooked in the statistical literature. This paper is devoted to that model. Some statistical measures of the distribution are expressed in closed form and it is shown that the model has increasing failure rate and strictly positive memory. Moreover, the members of this family of distributions can be ordered in terms of the hazard rate order. With respect to the parameter estimation, a problem of identifiability was found via Monte Carlo simulation, which is due to the existence of two shape parameters. Such a problem is overcome if one of the parameters is assumed to be known and then the maximum likelihood method provides accurate estimates. Rainfall data sets from the Australian Bureau of Meteorology are used to illustrate that the model under consideration may be an interesting alternative to other probability distributions commonly used for modeling non-negative real data. [ABSTRACT FROM AUTHOR]

Line transect survey methodology is a commonly used method for estimating the population abundance. Despite recent advances in this regard, parametric models are still widely used among biometricians, mainly because of their simplicity. In this paper, a new two-parameter detection model satisfying the shoulder conditions is proposed for modeling line transect data. We discuss its properties of interest, including the shapes of the model and the corresponding probability density function, moments, and the related sub-detection model. Maximum likelihood estimation of the parameters is considered. Subsequently, an application is carried out to the proposed model based on a practical data set of perpendicular distances. It is compared with some classical and recent models based on the evaluation of some goodness-of-fit statistics. As results, the variance-covariance matrix, confidence intervals of the parameters and estimated population abundance of the data set are obtained under the proposed detection model. [ABSTRACT FROM AUTHOR]

Zero-inflated models have become a popular tool for assessing relationships between explanatory variables and a zero-inflated count outcome. In these models, regression coefficients have latent class interpretations, where latent classes correspond to a susceptible subpopulation with observations generated from a count distribution and a non susceptible subpopulation that provides only zeros. However, it is often of interest to evaluate covariates effects in the overall mixture population, that is, on the marginal mean of the zero-inflated count. Marginal zero-inflated models, such as the marginal zero-inflated Poisson models, have been developed for that purpose. They specify independent submodels for the susceptibility probability and the marginal mean of the count response. When the count outcome is bounded, it is tempting to formulate a marginal zero-inflated binomial model in the same fashion. This, however, is not possible, due to inherent constraints that relate, in the zero-inflated binomial model, the susceptibility probability and the latent and marginal means of the count outcome. In this paper, we propose a new marginal zero-inflated binomial regression model that accommodates these constraints. We investigate the maximum likelihood estimator in this model, both theoretically and by simulations. An application to the analysis of health-care demand is provided for illustration. [ABSTRACT FROM AUTHOR]

In this paper, the empirical likelihood-based inference is investigated with varying coefficient panel data models with fixed effect. A naive empirical likelihood ratio is firstly proposed after the fixed effect is corrected. The maximum empirical likelihood estimators for the coefficient functions are derived as well as their asymptotic properties. Wilk's phenomenon of this naive empirical likelihood ratio is proven under a undersmoothing assumption. To avoid the requisition of undersmoothing and perform an efficient inference, a residual-adjusted empirical likelihood ratio is further suggested and shown as having a standard chi-square limit distribution, by which the confidence regions of the coefficient functions are constructed. Another estimators for the coefficient functions, together with their asymptotic properties, are considered by maximizing the residual-adjusted empirical log-likelihood function under an optimal bandwidth. The performances of these proposed estimators and confidence regions are assessed through numerical simulations and a real data analysis. [ABSTRACT FROM AUTHOR]

This paper focuses on pretest and shrinkage estimation strategies for generalized autoregressive fractionally integrated moving average (GARFIMA) models when some of the regression parameters are possible to restrict to a subspace. These estimation strategies are constructed on the assumption that some covariates are not statistically significant for the response. To define the pretest and shrinkage estimators, we fit two models: one includes all the covariates and the others are subject to linear constraint based on the auxiliary information of the insignificant covariates. The unrestricted and restricted estimators are then combined optimally to get the pretest and shrinkage estimators. We enlighten the statistical properties of the shrinkage and pretest estimators in terms of asymptotic bias and risk. We examine the comparative performance of pretest and shrinkage estimators with respect to unrestricted maximum partial likelihood estimator (UMPLE). We show that the shrinkage estimators have a lower relative mean squared error as compared to the UMPLE when the number of significant covariates exceeds two. Monte Carlo simulations are conducted to examine the relative performance of the proposed estimators to the UMPLE. An empirical application is used for the usefulness of our proposed estimation strategies. [ABSTRACT FROM AUTHOR]

The consistency of the semi-parametric maximum likelihood estimator (SMLE) under the semi-parametric linear regression model with right-censoring data (SPLRRC model) has not been studied under the necessary and sufficient condition for the identifiability of the parameters. In this paper, we discuss the necessary and sufficient condition for the consistency of SMLE under type I right censoring. [ABSTRACT FROM AUTHOR]

By establishing a connection between a quantile regression and an asymmetric Laplace distribution (ALD), this paper considers the maximum likelihood estimation of parameters of a quantile autoregression model with Markovian switching (MSQAR), where the error terms obey ALD whose scale parameter depends on regime shifts. By utilizing the mixture representation of ALD, we develop an effective ML approach for estimating parameters of MSQAR models, and obtain closed-form estimators of unknown parameters via the EM algorithm. Consistency and asymptotic normality of estimators are shown by extending some techniques adopted in Douc, Moulines, and Rydén (2004). Also, we extend some asymptotic results of estimators to the case where the conditional quantile regression model is misspecified. Furthermore, the proposed approach is illustrated by simulations and empirical data. Simulation results show that the procedure performs well in finite samples, and the empirical analysis not only supports the existence of regime-switching in the quantile autoregression model, but also has a good performance on data fitting. [ABSTRACT FROM AUTHOR]

The zero-inflated models have becomes fairly popular in the research literature. Medical and public health research involve the analysis of count data that exhibits a substantially large proportion of zeroes. The first zero-inflated model is the zero-inflated Poisson model, which concerns a random event containing excess zero-count in unit time. In this paper we consider a zero-inflated version of the modified hyper-Poisson distribution as a generalization of the zero-inflated Hyper-Poisson distribution of Kumar and Ramachandran (Commun.Statist.Simul.Comp., 2019) and study some of its important properties through deriving its probability generating function and expressions for factorial moments, mean, variance, recursion formulae for factorial moments, raw moments and probabilities. The estimation of the parameters of the proposed distribution is attempted and it has been fitted to certain real life data sets to test its goodness of fit. Further, certain test procedures are constructed for examining the significance of the parameters of the model and a simulation study is carried out for assessing the performance of the maximum likelihood estimators of the parameters of the distribution. [ABSTRACT FROM AUTHOR]

In this paper, we revisit the g and h control charts that are commonly used for monitoring the number of conforming cases between the two consecutive appearances of nonconformities. It is known that the process parameter of these charts is usually unknown and estimated by using the maximum likelihood estimator and the minimum variance unbiased estimator. However, the minimum variance unbiased estimator in the control charts has been inappropriately used in the quality engineering literature. This observation motivates us to provide the correct minimum variance unbiased estimator and investigate the theoretical and empirical biases of these estimators under consideration. Given that these charts are developed based on the underlying assumption that samples from the process should be balanced, which is often not satisfied in practice, we propose a method for constructing these charts with unbalanced samples. Finally, two real-data applications are provided for illustrative purposes. [ABSTRACT FROM AUTHOR]

The length-biased Birnbaum-Saunders distribution is both useful and practical for environmental sciences. In this paper, we initially derive some new properties for the length-biased Birnbaum-Saunders distribution, showing that one of its parameters is the mode and that it is bimodal. We then introduce a new regression model based on this distribution. We implement the maximum likelihood method for parameter estimation, approach interval estimation and consider three types of residuals. An elaborate Monte Carlo study is carried out for evaluating the performance of the likelihood-based estimates, the confidence intervals and the empirical distribution of the residuals. Finally, we illustrate the proposed regression model with the use of a real meteorological data set. [ABSTRACT FROM AUTHOR]

In this paper, we introduce six Weibull based mixture distributions to model income data. Several statistical properties of these models are derived and their closed forms are presented. The mixture model parameters are estimated using the maximum likelihood method and their performances are assessed with respect to average income per tax unit data for ten countries using information based criteria approaches as well as graphical observations. In addition, we provide application of these models to two popular inequality measures, the Gini and Bonferroni indexes as well as the common generalized entropy index. Analytic expressions of the poverty measures are given for head-count ratio and poverty-gap ratio. All the mixture models show good fit to the data with close proximity to empirical Gini and Bonferroni indexes in almost all ten countries where the income data sets are studied. [ABSTRACT FROM AUTHOR]

In analysis of variance (ANOVA) models, it is generally assumed that the distribution of the error terms is normal with mean zero and constant variance σ 2. Traditionally, a least square (LS) method is used for estimating the unknown parameters and testing the null hypothesis. It is known that, when the normality assumption is not satisfied, LS estimators of the parameters and the test statistics based on them lose their efficiency, see Tukey. On the other hand, a non constant variance problem which is called heteroskedasticity is another serious issue for LS estimators. The LS estimators still remain unbiased but the estimated standard error (SE) is wrong. Because of this, confidence intervals and hypotheses tests cannot be relied on. Welch's ANOVA is the most popular method to solve this problem. In this paper, we assume that the distribution of the error terms is skew-t with non constant variance in one-way ANOVA. We also propose a new test statistics based on the maximum likelihood (ML) estimators of skew-t distribution. A Monte Carlo simulation study is performed to compare traditional LS and Welch's method with the proposed method in terms of Type I errors and the powers. At the end of this study, an example is given for the illustration of the methods. [ABSTRACT FROM AUTHOR]

The censored exponential regression model is commonly used for modeling lifetime data. In this paper, we derive a simple matrix formula for the second-order covariance matrix of the maximum likelihood estimators in this class of regression models. The general matrix formula covers many types of censoring commonly encountered in practice. Also, the formula only involves simple operations on matrices and hence is quite suitable for computer implementation. Monte Carlo simulations are provided to show that the second-order covariances can be quite pronounced in small to moderate sample sizes. Additionally, based on the second-order covariance matrix, we propose an alternative Wald statistic to test hypotheses in this class of regression models. Monte Carlo simulation experiments reveal that the alternative Wald test exhibits type I error probability closer to the chosen nominal level. We also present an empirical application for illustrative purposes. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the partially linear varying-coefficient quantile regression model with observations missing at random (MAR), which include the responses or the responses and covariates MAR. Based on the local linear estimation of the varying-coefficient function in the model, we construct empirical log-likelihood ratio functions for unknown parameter in the linear part of the model, which are proved to be asymptotically weighted chi-squared distributions, further the adjusted empirical log-likelihood ratio functions are verified to converge to standard chi-squared distribution. The asymptotic normality of maximum empirical likelihood estimator for the parameter is also established. In order to do variable selection, we consider penalized empirical likelihood by using smoothly clipped absolute deviationv (SCAD) penalty, and the oracle property of the penalized likelihood estimator of the parameter is proved. Furthermore, Monte Carlo simulation and a real data analysis are undertaken to test the performance of the proposed methods. [ABSTRACT FROM AUTHOR]

The consistency of various estimators under the semi-parametric linear regression model and the standard right censorship model (SPLRRC model) has been studied under various assumptions since the 1970s. These assumptions are somewhat sufficient conditions for the identifiability of the parameters under the SPLRRC model. Since then, it has been a difficult open problem in survival analysis to find the necessary and sufficient condition for the identifiability of the parameters under the SPLRRC model. The open problem is solved in this paper. It is of interest to investigate whether the common estimators under this model are consistent under the identifiability condition. Under the latter condition, we show that the Buckley–James estimator and quantile regression estimator can be inconsistent and present partial results on the consistency of the semi-parametric maximum likelihood estimator. [ABSTRACT FROM AUTHOR]

The additive hazards model is one of the commonly used models for failure time data analysis and many authors have discussed its estimation under various situations. In this paper, we consider the same problem but under some inequality constraints when one faces current status data, for which it does not seem to exist an established estimation procedure due to the difficulties involved. In particular, the restricted maximum likelihood estimation approach is derived and the asymptotic properties of the resulting estimator of regression parameters are established with the use of some optimization methods. Simulation studies are conducted to assess the finite-sample performance of the proposed method and suggest that it works well for practical situations. A real data application is provided to demonstrate the utility of the proposed approach. [ABSTRACT FROM AUTHOR]

Recently, Lee and Cha proposed two general classes of discrete bivariate distributions. They have discussed some general properties and some specific cases of their proposed distributions. In this paper we have considered one model, namely bivariate discrete Weibull distribution, which has not been considered in the literature yet. The proposed bivariate discrete Weibull distribution is a discrete analogue of the Marshall–Olkin bivariate Weibull distribution. We study various properties of the proposed distribution and discuss its interesting physical interpretations. The proposed model has four parameters, and because of that it is a very flexible distribution. The maximum likelihood estimators of the parameters cannot be obtained in closed forms, and we have proposed a very efficient nested EM algorithm which works quite well for discrete data. We have also proposed augmented Gibbs sampling procedure to compute Bayes estimates of the unknown parameters based on a very flexible set of priors. Two data sets have been analyzed to show how the proposed model and the method work in practice. We will see that the performances are quite satisfactory. Finally, we conclude the paper. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the maximum likelihood estimation for the reflected Ornstein-Uhlenbeck processes with jumps based on continuous observations. We derive likelihood functions by using semimartingale theory. From this we get explicit formulas for estimators. The strong consistence and asymptotic normality of estimators are proved by using the method of stochastic integration. [ABSTRACT FROM AUTHOR]

In this paper, the novel estimating methods and their properties for pth-order dependence-driven random coefficient integer-valued autoregressive time series model (DDRCINAR(p)) are studied as the innovation sequence has a Poisson distribution and the thinning is binomial. Strict stationarity and ergodicity for DDRCINAR(p) model are proved. Conditional maximum likelihood and conditional least squares are used to estimate the model parameters. Asymptotic normality of the proposed estimators are derived. Finite sample properties of the conditional maximum likelihood estimator are examined in relation to the widely used conditional least squares estimator. It is concluded that, if the Poisson assumption can be justified, conditional maximum likelihood method performs better in terms of bias and MSE. Finally, three real data sets are analyzed to demonstrate the practical relevance of the model. [ABSTRACT FROM AUTHOR]

In this paper, we price a compound option with log asset price following an extended variance gamma process. The extended variance gamma process can control the skewness and kurtosis. The parameters of the model are estimated via the maximum likelihood method from historical data. We start with finding the risk neutral Esscher measure under which the discounted asset price process is a martingale. Then we derive an analytical pricing formula for compound option in terms of the Fourier integral of the characteristic function of extended variance gamma process, and we use this formula, in combination with the FFT algorithm, to calculate the compound option price across the whole spectrum of the exercise price. Finally, we present some numerical results for illustration. [ABSTRACT FROM AUTHOR]

In this paper a family of Wald-type test statistics for linear hypotheses in the logistic regression model with complex sample survey data is introduced and its properties are explored. The family of tests considered is based on the pseudo minimum phi-divergence estimator that contains, as a particular case, the pseudo maximum likelihood estimator. We obtain the asymptotic distribution and through a simulation study it is shown that some Wald-type tests present much more stable levels than the classical one for high and moderate values of the intra-cluster correlation parameter. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the multi-sample progressive Type-I censoring model where k ≥ 2 independent progressively Type-I censored experiments are conducted. The main objective is the derivation of the exact distribution of the maximum likelihood estimator (MLE) of the scale parameter when the lifetimes are exponentially distributed. The presented results provide also an alternative proof for the exact distribution of the MLE in the situation of a single progressively Type-I censored sample. Further, we use this result to construct exact confidence intervals for the scale parameter. In particular, the required stochastic monotonicity of the MLE is shown. [ABSTRACT FROM AUTHOR]

In this paper, a multicomponent system which has k independent and identical strength components X 1 , X 2 , ... , X k is considered. Each component is exposed to a common random stress Y when distributions are generalized logistic. This system is operating or failing only if at least s out of k ( 1 ≤ s ≤ k ) strength variables exceeds the random stress. The Bayesian and classical inferences of multicomponent stress-strength reliability under the generalized logistic distribution are studied. The small sample comparison of the reliability estimates is made through Monte Carlo simulation and asymptotic confidence interval is obtained based on maximum likelihood estimation. Also the highest posterior density credible interval is calculated based on Bayesian estimation with Gibbs and Metropolis Hastings algorithms. Finally analysis of a real data set has been presented for illustrative purposes too. [ABSTRACT FROM AUTHOR]

The asymptotic normality of a fixed number of the maximum likelihood estimators in a network model with degree heterogeneity and homophily has been established recently. In this paper, we further derive a central limit theorem for a linear combination of all the maximum likelihood estimators of degree parameter with degree heterogeneity and homophily when the number of nodes goes to infinity. Simulation studies are provided to illustrate the asymptotic results. [ABSTRACT FROM AUTHOR]

Extreme value theory models have found applications in myriad fields. Maximum likelihood (ML) is attractive for fitting the models because it is statistically efficient and flexible. However, in small samples, ML is biased to O(N-1) and some classical hypothesis tests suffer from size distortions. This paper derives the analytical Cox-Snell bias correction for the generalized extreme value (GEV) model, and for the model's extension to multiple order statistics (GEVr). Using simulations, the paper compares this correction to bootstrap-based bias corrections, for the generalized Pareto, GEV, and GEVr. It then compares eight approaches to inference with respect to primary parameters and extreme quantiles, some including corrections. The Cox-Snell correction is not markedly superior to bootstrap-based correction. The likelihood ratio test appears most accurately sized. The methods are applied to the distribution of geomagnetic storms. [ABSTRACT FROM AUTHOR]

The posterior corneal curvature and many other medical, environmental, and ecological variables are measured with angles where its range is less than π. Such data are so-called axial or half circular data. Half circular data modeling has not received much attention from researchers. This paper proposes a new half circular distribution model based on inverse stereographic projection technique of Burr-XII distribution. The maximum likelihood estimates of parameters are obtained and a simulation study to evaluate the performance of estimates was carried out. The application on the posterior corneal curvature of 23 patients shows that the proposed distribution fits the data well. [ABSTRACT FROM AUTHOR]

Recently, Cook et al. proposed a semiparametric likelihood estimator to improve study efficiency for a kind of survival data with covariate entries missing not at random (MNAR). Readily available supplementary information on the covariate is utilized in the estimation. They assume that the conditional distributions of the covariate X that having missing entry given the completely observed covariate Z, G 0 (· | Z) , is known. Guo et al. suggested to replace G 0 (· | Z) with its consistent estimator in the likelihood equation when G 0 (· | Z) is unknown. However, they did not derive the asymptotic theory of the resulted estimator in this case. This paper fills the gap. The theoretical development makes use of the theory of modern empirical process. [ABSTRACT FROM AUTHOR]

In this paper, we use extensive empirical data sets from Shanghai 50ETF (SH50ETF) and SH50ETF options markets in China to study how regime-switching jump-diffusion models improve goodness of fit and option pricing performance. Firstly, the model parameters are estimated by using maximum likelihood estimation and the numerical analysis indicates that the regime-switching jump-diffusion models outperform a range of other models. Secondly, the analytical option pricing formulae are obtained via the fast Fourier transform and the empirical results using the proposed option pricing formulae are presented. Finally, we find that the calculated option prices are fairly consistent with the actual market prices. [ABSTRACT FROM AUTHOR]

This paper introduces a novel model with six parameters called "flexible additive Weibull distribution (FAWD)." The suggested model is capable to model the life time data with a non-monotonic hazard rate. The statistical properties of the new distribution including Renyi entropy, quantile function, maximum likelihood estimation, order statistics, moment generating function, probability generating function, factorial and characteristic function are discussed in details. The flexibility of the proposed distribution is judged based on AIC, CAIC, BIC and HQIC, the smaller is the value of these statistics, and the better is the results. The usefulness of the proposed distribution is illustrated by using two real data sets. The proposed distribution has shown better performance and fits the used data better than some other well-known distributions. [ABSTRACT FROM AUTHOR]

In this paper, we first consider the pseudo maximum likelihood estimation of the univariate GARCH (2,2) model and derive the underlying estimator. Then, we make use of the technique of martingales to establish the asymptotic normality of the pseudo-maximum likelihood estimator (PMLE) of the univariate GARCH (2,2) model. Contrary to previous approaches encountered in the statistical literature, the pseudo-likelihood function uses the general form of the density laws of the quadratic exponential family. [ABSTRACT FROM AUTHOR]

The problems of existence and uniqueness of maximum likelihood estimates for logistic regression were completely solved by Silvapulle in 1981 and Albert and Anderson in 1984. In this paper, we extend the well-known results by Silvapulle and by Albert and Anderson to weighted logistic regression. We analytically prove the equivalence between the overlap condition used by Albert and Anderson and that used by Silvapulle. We show that the maximum likelihood estimate of weighted logistic regression does not exist if there is a complete separation or a quasicomplete separation of the data points, and exists and is unique if there is an overlap of data points. Our proofs and results for weighted logistic apply to unweighted logistic regression. [ABSTRACT FROM PUBLISHER]

One provides in this paper the pseudo-likelihood estimator (PMLE) and asymptotic theory for the GARCH (1,1) process. Strong consistency of the pseudo-maximum-likelihood estimator (MLE) is established by appealing to conditions given in Jeantheau (1998) concerning the existence of a stationary and ergodic solution to the multivariate GARCH (p, q) process. One proves the asymptotic normality of the PMLE by appealing to martingales' techniques. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]