A Model Validation Procedure when Covariate Data are Missing at Random

Abstract. In the presence of missing covariates, standard model validation procedures may result in misleading conclusions. By building generalized score statistics on augmented inverse probability weighted complete‐case estimating equations, we develop a new model validation procedure to assess the adequacy of a prescribed analysis model when covariate data are missing at random. The asymptotic distribution and local alternative efficiency for the test are investigated. Under certain conditions, our approach provides not only valid but also asymptotically optimal results. A simulation study for both linear and logistic regression illustrates the applicability and finite sample performance of the methodology. Our method is also employed to analyse a coronary artery disease diagnostic dataset.     

Bootstrap confidence intervals of CNpk for inverse Rayleigh and log-logistic distributions

In this article bootstrap confidence intervals of process capability index as suggested by Chen and Pearn [An application of non-normal process capability indices. Qual Reliab Eng Int. 1997;13:355–360] are studied through simulation when the underlying distributions are inverse Rayleigh and log-logistic distributions. The well-known maximum likelihood estimator is used to estimate the parameter. The bootstrap confidence intervals considered in this paper consists of various confidence intervals. A Monte Carlo simulation has been used to investigate the estimated coverage probabilities and average widths of the bootstrap confidence intervals. Application examples on two distributions for process capability indices are provided for practical use.     

Asymptotically refined score and GOF tests for inverse Gaussian models

ABSTRACT

The score test and the GOF test for the inverse Gaussian distribution, in particular the latter, are known to have large size distortion and hence unreliable power when referring to the asymptotic critical values. We show in this paper that with the appropriately bootstrapped critical values, these tests become second-order accurate, with size distortion being essentially eliminated and power more reliable. Two major generalizations of the score test are made: one is to allow the data to be right-censored, and the other is to allow the existence of covariate effects. A data mapping method is introduced for the bootstrap to be able to produce censored data that are conformable with the null model. Monte Carlo results clearly favour the proposed bootstrap tests. Real data illustrations are given.     

A non-iterative sampling Bayesian method for linear mixed models with normal independent distributions

In this paper, we utilize normal/independent (NI) distributions as a tool for robust modeling of linear mixed models (LMM) under a Bayesian paradigm. The purpose is to develop a non-iterative sampling method to obtain i.i.d. samples approximately from the observed posterior distribution by combining the inverse Bayes formulae, sampling/importance resampling and posterior mode estimates from the expectation maximization algorithm to LMMs with NI distributions, as suggested by Tan et al. [33 Tan, M., Tian, G. and Ng, K. 2003. A noniterative sampling method for computing posteriors in the structure of EM-type algorithms. Statist. Sinica, 13(3): 625–640. [Web of Science ®] , [Google Scholar]]. The proposed algorithm provides a novel alternative to perfect sampling and eliminates the convergence problems of Markov chain Monte Carlo methods. In order to examine the robust aspects of the NI class, against outlying and influential observations, we present a Bayesian case deletion influence diagnostics based on the Kullback–Leibler divergence. Further, some discussions on model selection criteria are given. The new methodologies are exemplified through a real data set, illustrating the usefulness of the proposed methodology.     

Comparing Normal Random Samples,with Uncertainty About the Priors and Utilities

Abstract. We study the problem of deciding which of two normal random samples, at least one of them of small size, has greater expected value. Unlike in the standard Bayesian approach, in which a single prior distribution and a single loss function are declared, we assume that a set of plausible priors and a set of plausible loss functions are elicited from the expert (the client or the sponsor of the analysis). The choice of the sample that has greater expected value is based on equilibrium priors, allowing for an impasse if for some plausible priors and loss functions choosing one and for others the other sample is associated with smaller expected loss.     

基于梯度统计量的逆抽样下风险差的置信区间构建

通过逆抽样过程获得的分布又称为负二项分布,在流行病学研究和二分类变量分布的研究中应用极为广泛。因此,提出两种基于梯度统计量的逆抽样下风险差的置信区间的构建方法,分别依据风险差的极大似然估计(MLE)和方差最小无偏一致估计量(UMVUE)。与现有的WALD方法和得分方法相比,该方法所构建置信区间的优点在于:置信区间构建方法既不需要计算Fisher信息阵也不需要计算其逆矩阵,可使计算得以大大简化;对所提出的基于梯度统计量的置信区间构建方法进行蒙特卡洛模拟研究,模拟结果表明提出的构建方法可以得到很好的覆盖概率和较短的区间宽度。     

Improved kth power expectile regression with nonignorable dropouts

The kth ( 1<k≤2) power expectile regression (ER) can balance robustness and effectiveness between the ordinary quantile regression and ER simultaneously. Motivated by a longitudinal ACTG 193A data with nonignorable dropouts, we propose a two-stage estimation procedure and statistical inference methods based on the kth power ER and empirical likelihood to accommodate both the within-subject correlations and nonignorable dropouts. Firstly, we construct the bias-corrected generalized estimating equations by combining the kth power ER and inverse probability weighting approaches. Subsequently, the generalized method of moments is utilized to estimate the parameters in the nonignorable dropout propensity based on sufficient instrumental estimating equations. Secondly, in order to incorporate the within-subject correlations under an informative working correlation structure, we borrow the idea of quadratic inference function to obtain the improved empirical likelihood procedures. The asymptotic properties of the corresponding estimators and their confidence regions are derived. The finite-sample performance of the proposed estimators is studied through simulation and an application to the ACTG 193A data is also presented.     

非线性反问题同伦反演的一般格式

针对非线性算子参数识别反问题,引入具有大范围收敛特性的同伦算法,构造了同伦反演求解的一般格式。     

Independent screening in high-dimensional exponential family predictors’ space

We present a methodology for screening predictors that, given the response, follow a one-parameter exponential family distributions. Screening predictors can be an important step in regressions when the number of predictors p is excessively large or larger than n the number of observations. We consider instances where a large number of predictors are suspected irrelevant for having no information about the response. The proposed methodology helps remove these irrelevant predictors while capturing those linearly or nonlinearly related to the response.     

An Inverse‐regression Method of Dependent Variable Transformation for Dimension Reduction with Non‐linear Confounding

Many model‐free dimension reduction methods have been developed for high‐dimensional regression data but have not paid much attention on problems with non‐linear confounding. In this paper, we propose an inverse‐regression method of dependent variable transformation for detecting the presence of non‐linear confounding. The benefit of using geometrical information from our method is highlighted. A ratio estimation strategy is incorporated in our approach to enhance the interpretation of variable selection. This approach can be implemented not only in principal Hessian directions (PHD) but also in other recently developed dimension reduction methods. Several simulation examples that are reported for illustration and comparisons are made with sliced inverse regression and PHD in ignorance of non‐linear confounding. An illustrative application to one real data is also presented.