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.     

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.     

Influence Diagnostics of Semiparametric Nonlinear Reproductive Dispersion Models

This article proposes a semiparametric nonlinear reproductive dispersion model (SNRDM) which is an extension of nonlinear reproductive dispersion model and semiparametric regression model. Maximum penalized likelihood estimators (MPLEs) of unknown parameters and nonparametric functions in SNRDMs are presented. Some novel diagnostic statistics such as Cook distance and difference deviance for parametric and nonparametric parts are developed to identify influence observations in SNRDMs on the basis of case-deletion method, and some formulae readily computed with the MPLEs algorithm for diagnostic measures are given. The equivalency of case-deletion models and mean-shift outlier models in SNRDM is investigated. A simulation study and a real example are used to illustrate the proposed diagnostic measures.     

Empirical Likelihood Inference for the Parameter in Additive Partially Linear EV Models

In this article, we consider empirical likelihood inference for the parameter in the additive partially linear models when the linear covariate is measured with error. By correcting for attenuation, a corrected-attenuation empirical log-likelihood ratio statistic for the unknown parameter β, which is of primary interest, is suggested. We show that the proposed statistic is asymptotically standard chi-square distribution without requiring the undersmoothing of the nonparametric components, and hence it can be directly used to construct the confidence region for the parameter β. Some simulations indicate that, in terms of comparison between coverage probabilities and average lengths of the confidence intervals, the proposed method performs better than the profile-based least-squares method. We also give the maximum empirical likelihood estimator (MELE) for the unknown parameter β, and prove the MELE is asymptotically normal under some mild conditions.     

A Weighting Approach for GEE Analysis with Missing Data

We propose a new weighting (WT) method to handle missing categorical outcomes in longitudinal data analysis using generalized estimating equations (GEE). The proposed WT provides a valid GEE estimator when the data are missing at random (MAR), and has more stable weights and shows advantage in efficiency compared to the inverse probability weighing method in the presence of small observation probabilities. The WT estimator is similar to the stabilized weighting (SWT) estimator under mild conditions, but it is more stable and efficient than SWT when the associations of the outcome with the observation probabilities and the covariate are strong.     

An Extension of Economic Design of x-Bar Control Charts for Non Normally Distributed Data Under Weibull Shock Models

Three parameters—sample size, sampling intervals, and the control limits—must be determined when the x bar chart to monitor a manufacturing process. The constant sampling intervals were widely employed because of its administrative simplicity. However, the variable sampling interval (VSI) has recently been shown to give substantially faster detection of most process shifts than fixed-sampling-interval (FSI) for x-bar charts. In addition, these measurements in the subgroup are assumed to be normally distributed. That assumption may not be tenable. This investigation compares the economic design of x-bar control charts for non normal data under Weibull shock models with various sampling avenues.     

Adaptive Lasso Variable Selection for the Accelerated Failure Models

This article considers the adaptive lasso procedure for the accelerated failure time model with multiple covariates based on weighted least squares method, which uses Kaplan-Meier weights to account for censoring. The adaptive lasso method can complete the variable selection and model estimation simultaneously. Under some mild conditions, the estimator is shown to have sparse and oracle properties. We use Bayesian Information Criterion (BIC) for tuning parameter selection, and a bootstrap variance approach for standard error. Simulation studies and two real data examples are carried out to investigate the performance of the proposed method.     

An Application of Matrix Power Series to Linear Models

In the system of two seemingly unrelated regressions, employing a matrix power series, we show that the two-stage estimator is better than the ordinary least square estimator (OLSE) in terms of the mean square error matrix (MSEM) criterion. The result enriches the existing literature and can be applied to many fields of applications related to economics and statistics.     

Objective Priors for Parameters in a Normal Linear Regression with Measurement Error

We investigate certain objective priors for the parameters in a normal linear regression models with one of the explanatory variables subject to measurement error. We first show that the use of the standard non informative prior for normal linear regression without measurement error leads to an improper posterior in the measurement error model. We then derive the Jeffreys prior and reference priors, and show that they lead to proper posteriors. We use simulation study to compare the frequentist performance of the estimates derived using these priors, and the MLE.