Dirichlet Processes in Nonlinear Mixed Effects Models

In this article, we use two efficient approaches to deal with the difficulty in computing the intractable integrals when implementing Gibbs sampling in the nonlinear mixed effects model (NLMM) based on Dirichlet processes (DP). In the first approach, we compute the Laplace's approximation to the integral for its high accuracy, low cost, and ease of implementation. The second approach uses the no-gaps algorithm of MacEachern and Müller (1998 MacEachern , S. , Müller , P. ( 1998 ). Estimating mixtures of Dirichlet process models . Journal of Computational and Graphical Statistics 7 : 223 – 238 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) to perform Gibbs sampling without evaluating the difficult integral. We apply both approaches to real problems and simulations. Results show that both approaches perform well in density estimation and prediction and are superior to the parametric analysis in that they can detect important model features, such as skewness, long tails, and multimodality, whereas the parametric analysis cannot.     

A Shrinkage Estimation of Central Subspace in Sufficient Dimension Reduction

Sliced regression is an effective dimension reduction method by replacing the original high-dimensional predictors with its appropriate low-dimensional projection. It is free from any probabilistic assumption and can exhaustively estimate the central subspace. In this article, we propose to incorporate shrinkage estimation into sliced regression so that variable selection can be achieved simultaneously with dimension reduction. The new method can improve the estimation accuracy and achieve better interpretability for the reduced variables. The efficacy of proposed method is shown through both simulation and real data analysis.     

A Note on the Likelihood Ratio Test for Equality of k Normal Populations

The authors derive the analytic expressions for the mean and variance of the log-likelihood ratio for testing equality of k (k ≥ 2) normal populations, and suggest a chi-square approximation and a gamma approximation to the exact null distribution. Numerical comparisons show that the two approximations and the original beta approximation of Neyman and Pearson (1931 Neyman , J. , Pearson , E. S. ( 1931 ). On the problem of k samples . In: Neyman , J. , Pearson , E. S. , eds. Joint Statistical Papers . Cambridge : Cambridge University Press , pp. 116 – 131 . [Google Scholar]) are all accurate, and the gamma approximation is the most accurate.     

Partially Accelerated Life Tests for the Weibull Distribution Under Multiply Censored Data

This article aims to estimate the parameters of the Weibull distribution in step-stress partially accelerated life tests under multiply censored data. The step partially acceleration life test is that all test units are first run simultaneously under normal conditions for a pre-specified time, and the surviving units are then run under accelerated conditions until a predetermined censoring time. The maximum likelihood estimates are used to obtaining the parameters of the Weibull distribution and the acceleration factor under multiply censored data. Additionally, the confidence intervals for the estimators are obtained. Simulation results show that the maximum likelihood estimates perform well in most cases in terms of the mean bias, errors in the root mean square and the coverage rate. An example is used to illustrate the performance of the proposed approach.     

Comparing a New Gini Test with Other Symmetry Tests When Median Is Unknown

Although there exists an ample literature on the tests of univariate symmetry, each article provides comparison of few selected competitors only. We are comparing the performance of 15 tests recommended in the literature and two new methods introduced by Auda (2006 Auda (Ouda), H. 2006. New Tests of Univariate Symmetry Based on the Gini Mean Difference, Kalamazoo, MI: Western Michigan University. Ph.D. thesis [Google Scholar]). One of them, rank-based test RS, compares favorably with several existing procedures in controlling the Type I error as well as in power as shown in our comprehensive simulation study. An important novelty in the article are Figs. 1– 3 enabling comparison of Type I error probabilities and power of the 16 tests for 17 null and 19 alternative distributions.     

Approximate Bayesian Computation for Exponential Random Graph Models for Large Social Networks

We consider the issue of sampling from the posterior distribution of exponential random graph (ERG) models and other statistical models with intractable normalizing constants. Existing methods based on exact sampling are either infeasible or require very long computing time. We study a class of approximate Markov chain Monte Carlo (MCMC) sampling schemes that deal with this issue. We also develop a new Metropolis–Hastings kernel to sample sparse large networks from ERG models. We illustrate the proposed methods on several examples.     

A simulation study of ridge and other regression estimators

We consider a number of estimators of regression coefficients, all of generalized ridge, or 'shrinkage' type. Results of a simulation study indicate that with respect to two commonly used mean square error criteria, two ordinary ridge estimators, one proposed by Hoerl, Kennard and Baldwin, and the other introduced here, perform substantially better than both least squares and the other estimators discussed here     

Change-Point Estimation in Long Memory Nonparametric Models with Applications

We consider the estimation of a change point or discontinuity in a regression function for random design model with long memory errors. We provide several change-point estimators and investigate the consistency of the estimators. Using the fractional ARIMA process as an example of long memory process, we report a small Monte Carlo experiment to compare the performance of the estimators in finite samples. We finish by applying the method to a climatological data example.     

Reliability Research of Dependent Failure Systems Using Copula

The computation of reliability characteristics of a system that consists of dependent components sometimes becomes difficult, especially when a specific type of dependence is not identified. In this paper, some systems with arbitrary dependent components are studied using copula. In the system, the components are dependent on each other and the dependent relations may be either linear or nonlinear correlation. The efficient formulas are presented to compute the reliability characteristics, such as reliability function, failure rate and meantime to failure of series, parallel and k-out-of-n systems. The reliability functions of dependant systems are compared with independent system. At last, the numerical examples are presented to illustrate the results obtained in this paper.     

A multiple-case deletion approach for detecting influential points in high-dimensional regression

ABSTRACT

In high-dimensional regression, the presence of influential observations may lead to inaccurate analysis results so that it is a prime and important issue to detect these unusual points before statistical regression analysis. Most of the traditional approaches are, however, based on single-case diagnostics, and they may fail due to the presence of multiple influential observations that suffer from masking effects. In this paper, an adaptive multiple-case deletion approach is proposed for detecting multiple influential observations in the presence of masking effects in high-dimensional regression. The procedure contains two stages. Firstly, we propose a multiple-case deletion technique, and obtain an approximate clean subset of the data that is presumably free of influential observations. To enhance efficiency, in the second stage, we refine the detection rule. Monte Carlo simulation studies and a real-life data analysis investigate the effective performance of the proposed procedure.