Likelihood-based and Bayesian methods for Tweedie compound Poisson linear mixed models

The Tweedie compound Poisson distribution is a subclass of the exponential dispersion family with a power variance function, in which the value of the power index lies in the interval (1,2). It is well known that the Tweedie compound Poisson density function is not analytically tractable, and numerical procedures that allow the density to be accurately and fast evaluated did not appear until fairly recently. Unsurprisingly, there has been little statistical literature devoted to full maximum likelihood inference for Tweedie compound Poisson mixed models. To date, the focus has been on estimation methods in the quasi-likelihood framework. Further, Tweedie compound Poisson mixed models involve an unknown variance function, which has a significant impact on hypothesis tests and predictive uncertainty measures. The estimation of the unknown variance function is thus of independent interest in many applications. However, quasi-likelihood-based methods are not well suited to this task. This paper presents several likelihood-based inferential methods for the Tweedie compound Poisson mixed model that enable estimation of the variance function from the data. These algorithms include the likelihood approximation method, in which both the integral over the random effects and the compound Poisson density function are evaluated numerically; and the latent variable approach, in which maximum likelihood estimation is carried out via the Monte Carlo EM algorithm, without the need for approximating the density function. In addition, we derive the corresponding Markov Chain Monte Carlo algorithm for a Bayesian formulation of the mixed model. We demonstrate the use of the various methods through a numerical example, and conduct an array of simulation studies to evaluate the statistical properties of the proposed estimators.     

Reducing bias of the maximum-likelihood estimation for the truncated Pareto distribution

The Pareto distribution is an important distribution in statistics, which has been widely used in finance, physics, hydrology, geology, astronomy, and so on. Even though the parameter estimation for the Pareto distribution has been well established in the literature, the estimation problem for the truncated Pareto distribution becomes complex. This article investigates the bias and mean-squared error of the maximum-likelihood estimation for the truncated Pareto distribution, and some useful results are obtained.     

Model averaging for M-estimation

M-estimation is a widely used technique for robust statistical inference. In this paper, we study model selection and model averaging for M-estimation to simultaneously improve the coverage probability of confidence intervals of the parameters of interest and reduce the impact of heavy-tailed errors or outliers in the response. Under general conditions, we develop robust versions of the focused information criterion and a frequentist model average estimator for M-estimation, and we examine their theoretical properties. In addition, we carry out extensive simulation studies as well as two real examples to assess the performance of our new procedure, and find that the proposed method produces satisfactory results.     

A Multivariate Synthetic Control Chart for Monitoring the Process Mean Vector of Skewed Populations Using Weighted Standard Deviations

This article proposes a multivariate synthetic control chart for skewed populations based on the weighted standard deviation method. The proposed chart incorporates the weighted standard deviation method into the standard multivariate synthetic control chart. The standard multivariate synthetic chart consists of the Hotelling's T ² chart and the conforming run length chart. The weighted standard deviation method adjusts the variance–covariance matrix of the quality characteristics and approximates the probability density function using several multivariate normal distributions. The proposed chart reduces to the standard multivariate synthetic chart when the underlying distribution is symmetric. In general, the simulation results show that the proposed chart performs better than the existing multivariate charts for skewed populations and the standard T ² chart, in terms of false alarm rates as well as moderate and large mean shift detection rates based on the various degrees of skewnesses.     

Operating Characteristics for Group Sequential Trials Monitored Under Fractional Brownian Motion

Brownian motion has been used to derive stopping boundaries for group sequential trials, however, when we observe dependent increment in the data, fractional Brownian motion is an alternative to be considered to model such data. In this article we compared expected sample sizes and stopping times for different stopping boundaries based on the power family alpha spending function under various values of Hurst coefficient. Results showed that the expected sample sizes and stopping times will decrease and power increases when the Hurst coefficient increases. With same Hurst coefficient, the closer the boundaries are to that of O'Brien-Fleming, the higher the expected sample sizes and stopping times are; however, power has a decreasing trend for values start from H = 0.6 (early analysis), 0.7 (equal space), 0.8 (late analysis). We also illustrate study design changes using results from the BHAT study.     

Semiparametric ROC surface estimation for continuous diagnostic tests via polytomous logistic regression procedures

In this paper, we propose a semiparametric method of estimating receiver operating characteristic (ROC) surfaces for continuous diagnostic tests under density ratio models. Implementation of our method is easy since the usual polytomous logistic regression procedures in many statistical software packages can be employed. A simulated example is provided to facilitate the implementation of our method. Simulation results show that the proposed semiparametric ROC surface estimator is more efficient than the nonparametric counterpart and the parametric counterpart whether the normality assumption of data holds or not. Moreover, some simulation results on the underlying semiparametric distribution function estimators are also reported. In addition, some discussions on the proposed method as well as analysis of a real data set are provided.     

Title Index

Abstract

This article describes how electronic resources have impacted the University of Nevada, Las Vegas (UNLV) Libraries' binding operation and how the libraries have responded to the resulting challenges, including the need for updated collection development and preservation/conservation policies, a comprehensive bindery contract, and a fully functional in-house binding capability. The evaluation of the binding process must continue as libraries move from a predominantly print to a predominantly electronic environment. Librarians, scholars, and binders should work together to preserve and bind library collections that will be valuable to future generations.     

Group Variable Selection with Oracle Property by Weight-Fused Adaptive Elastic Net Model for Strongly Correlated Data

This paper is the generalization of weight-fused elastic net (Fu and Xu, 2012 Fu, G., Xu, Q. (2012). Grouping variable selection by weight fused elastic net for multi-collinear data. Communications in Statistics-Simulation and Computation 41(2):205–221.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), which performs group variable selection by combining weight-fused LASSO(wfLasso) and elastic net (Zou and Hastie, 2005 Zou, H., Hastie, T. (2005). Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 67(2):301–320.[Crossref], [Web of Science ®] , [Google Scholar]) penalties. In this study, the elastic net penalty is replaced by adaptive elastic net penalty (AdaEnet) (Zou and Zhang, 2009 Zou, H., Zhang, H. (2009). On the adaptive elastic-net with a diverging number of parameters. Annals of Statistics 37(4):1733–1751.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), and a new group variable selection algorithm with oracle property (Fan and Li, 2001 Fan, J., Li, R. (2001). Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association 96(456):1348–1360.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]; Zou, 2006 Zou, H. (2006). The adaptive lasso and its oracle properties. Journal of the American Statistical Association 101(476):1418–1429.[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) is obtained.     

Almost Periodic Solutions for Stochastic Differential Equations Driven By G-Brownian Motion

In this paper, we introduce the concept of the p-mean almost periodicity for stochastic processes in non linear expectation spaces. The existence and uniqueness of square-mean almost periodic solutions to some non linear stochastic differential equations driven by G-Brownian motion are established under some assumptions for the coefficients. The asymptotic stability of the unique square-mean almost periodic solution in the square-mean sense is also discussed.