Optimum constant-stress life test plans for Pareto distribution under type-I censoring

The paper considers the case of constant-stress partially accelerated life testing (CSPALT) when two stress levels are involved under type-I censoring. The lifetimes of test items are assumed to follow a two-parameter Pareto lifetime distribution. Maximum-likelihood method is used to estimate the parameters of CSPALT model. Confidence intervals for the model parameters are constructed. Optimum CSPALT plans that determine the best choice of the proportion of test units allocated to each stress are developed. Such optimum test plans minimize the generalized asymptotic variance of the maximum-likelihood estimators of the model parameters. For illustration, Monte Carlo simulation studies are presented.     

Rounding non-binary categorical variables following multivariate normal imputation: evaluation of simple methods and implications for practice

We study bias arising from rounding categorical variables following multivariate normal (MVN) imputation. This task has been well studied for binary variables, but not for more general categorical variables. Three methods that assign imputed values to categories based on fixed reference points are compared using 25 specific scenarios covering variables with k=3, …, 7 categories, and five distributional shapes, and for each k=3, …, 7, we examine the distribution of bias arising over 100,000 distributions drawn from a symmetric Dirichlet distribution. We observed, on both empirical and theoretical grounds, that one method (projected-distance-based rounding) is superior to the other two methods, and that the risk of invalid inference with the best method may be too high at sample sizes n≥150 at 50% missingness, n≥250 at 30% missingness and n≥1500 at 10% missingness. Therefore, these methods are generally unsatisfactory for rounding categorical variables (with up to seven categories) following MVN imputation.     

Parametric simultaneous robust inferences for regression coefficient under generalized linear models

In this article, the parametric robust regression approaches are proposed for making inferences about regression parameters in the setting of generalized linear models (GLMs). The proposed methods are able to test hypotheses on the regression coefficients in the misspecified GLMs. More specifically, it is demonstrated that with large samples, the normal and gamma regression models can be properly adjusted to become asymptotically valid for inferences about regression parameters under model misspecification. These adjusted regression models can provide the correct type I and II error probabilities and the correct coverage probability for continuous data, as long as the true underlying distributions have finite second moments.     

The optimal allocation combination for the two-sided sequential screening procedure based on the individual misclassification error

In this paper, the expected total costs (ETCs) of three kinds of quality cost functions for the two-sided sequential screening procedure (SQSP) based on the individual misclassification error are obtained, where the ETC is the sum of the expected cost of inspection, the expected cost of rejection and the expected cost of quality. The general formulas for all the desired probabilities and three ETCs when k screening variables are allocated into r-stages are derived. The optimal allocation combination for each ETC is determined based on the criterion of minimum ETC. Finally, we give two examples to illustrate the selection of the optimal allocation combination for the SQSP.     

On the estimation of the extreme value and normal distribution parameters based on progressive type-II hybrid-censored data

A progressive hybrid censoring scheme is a mixture of type-I and type-II progressive censoring schemes. In this paper, we mainly consider the analysis of progressive type-II hybrid-censored data when the lifetime distribution of the individual item is the normal and extreme value distributions. Since the maximum likelihood estimators (MLEs) of these parameters cannot be obtained in the closed form, we propose to use the expectation and maximization (EM) algorithm to compute the MLEs. Also, the Newton–Raphson method is used to estimate the model parameters. The asymptotic variance–covariance matrix of the MLEs under EM framework is obtained by Fisher information matrix using the missing information and asymptotic confidence intervals for the parameters are then constructed. This study will end up with comparing the two methods of estimation and the asymptotic confidence intervals of coverage probabilities corresponding to the missing information principle and the observed information matrix through a simulation study, illustrated examples and real data analysis.     

On the monitoring of mixture simple linear profiles

ABSTRACT

In some applications, the quality of a process or product is best characterized by a functional relationship between a response variable and one or more explanatory variables. Profile monitoring is used to understand and to check the stability of this relationship or curve over time. In the existing simple linear regression profile models, it is often assumed that the data follow a single mode distribution and consequently the noise of the functional relationship follows a normal distribution. However, in some applications, it is likely that the data may follow a multiple-modes distribution. In this case, it is more appropriate to assume that the data follow a mixture profile. In this study, we focus on a mixture simple linear profile model, and propose new control schemes for Phase II monitoring. The proposed methods are shown to have good performance in a simulation study.     

Generating autocorrelated pseudo-random numbers with specific distributions

An easily implemented and computationally efficient procedure is presented for the generation of autocorrelated pseudo-random numbers with specific probability distributions. A plot illustrates the relationship among the autocorrelations of the uniform, Rayleigh, and exponential distributions corresponding to a given autocorrelation in the normal generating distribution.     

On intra-class correlation coefficient estimation

Consider the problem of estimating the intra-class correlation coefficient of a symmetric normal distribution. In a recent article (Pal and Lim (1999)) it has been shown that the three popular estimators, namely—the maximum likelihood estimator (MLE), the method of moments estimator (MME) and the unique minimum variance unbiased estimator (UMVUE), are second order admissible under the squared error loss function. In this paper we study the performance of the above mentioned estimators in terms of Pitman Nearness Criterion (PNC) as well as Stochastic Domination Criterion (SDC). We then apply the aforementioned estimators to two real life data sets with moderate to large sample sizes, and bootstrap bias as well as mean squared errors are computed to compare the estimators. In terms of overall performance the MME seems most appealing among the three estimators considered here and this is the main contribution of our paper. Formerly University of Southewestern Louisisna     

Approximate Bayesian Inference in Spatial Generalized Linear Mixed Models

Abstract.  In this paper we propose fast approximate methods for computing posterior marginals in spatial generalized linear mixed models. We consider the common geostatistical case with a high dimensional latent spatial variable and observations at known registration sites. The methods of inference are deterministic, using no simulation-based inference. The first proposed approximation is fast to compute and is 'practically sufficient', meaning that results do not show any bias or dispersion effects that might affect decision making. Our second approximation, an improvement of the first version, is 'practically exact', meaning that one would have to run MCMC simulations for very much longer than is typically done to detect any indication of error in the approximate results. For small-count data the approximations are slightly worse, but still very accurate. Our methods are limited to likelihood functions that give unimodal full conditionals for the latent variable. The methods help to expand the future scope of non-Gaussian geostatistical models as illustrated by applications of model choice, outlier detection and sampling design. The approximations take seconds or minutes of CPU time, in sharp contrast to overnight MCMC runs for solving such problems.