A MORE GENERAL CRITERION FOR SUBSET SELECTION IN MULTIPLE LINEAR REGRESSION

ABSTRACT

In this article, we propose a more general criterion called S_p -criterion, for subset selection in the multiple linear regression Model. Many subset selection methods are based on the Least Squares (LS) estimator of β, but whenever the data contain an influential observation or the distribution of the error variable deviates from normality, the LS estimator performs ‘poorly’ and hence a method based on this estimator (for example, Mallows’ C_p -criterion) tends to select a ‘wrong’ subset. The proposed method overcomes this drawback and its main feature is that it can be used with any type of estimator (either the LS estimator or any robust estimator) of β without any need for modification of the proposed criterion. Moreover, this technique is operationally simple to implement as compared to other existing criteria. The method is illustrated with examples.     

A Study of Suicide Risk Using a Cox Cure Model via a Retrospective Sampling and Multiple Imputation

The incidence of suicide is an example of rare event. A Cox cure model is adopted to examine the suicide risk of a cohort study of a sample of 65,000 Personal Emergency Link users over a 10-year observation period. Our objective is to investigate the effect of personal covariates on the failure time to suicide as well as the long-term survival from suicide. Based on the Cox cure model, a new and efficient estimation approach using retrospective sampling and multiple imputation was used. Compared with the standard Cox proportional hazards model, the Cox cure model provides a new perspective on analyzing the suicide data.     

“多元素养作文”初探

"多元素养作文"是在对作文教学现状反思以及对作文、作文教学再认识的基础上提出的作文课程设想.它是由"一向三维四元"构成的;其基本理念有目标理念、训练理念、资源理念;基本特征是训练的系统性、资源的开放性、形式的自主探究、过程的体验性、操作的互动性;它的训练体例由作文境域、个性体悟、路径辨析、创新呈现、反思交流组成.     

Quantitative refinements for comparisons of institutional performance

In the context of the data and issues discussed by Goldstein and Spiegelhalter, we suggest refinements which can be used by decision makers when confronted with ranking problems associated with 'league tables'. Two ranking criteria are defined and their performance illustrated for one of the studies reported by Goldstein and Spiegelhalter.     

Issues in the design and analysis of therapeutic trials in human immunodeficiency virus infection

The first randomized trial of antiviral therapy in human immunodeficiency virus (HIV) disease included 282 patients with acquired immune deficiency syndrome (AIDS) or AIDS-related complex and was stopped in 1986 after an average follow-up of 4 months because of a substantial reduction in mortality in the group who received zidovudine (AZT). The era of anti-HIV treatment had begun. This paper discusses some of the difficulties which have emerged over the subsequent 10 years as new anti-HIV drugs have been developed requiring evaluation in clinical trials. The trials in which the British Medical Research Council has played a major role (the Concorde, Alpha and Delta trials) and some of the key trials conducted by the AIDS Clinical Trials Group (ACTG) (the ACTG 019 and ACTG 175 trials) and the Community Programs for Clinical Research on AIDS (CPCRA) (the CPCRA 007 trial) in the US will be used to illustrate some of the issues faced by clinical trialists and governmental regulatory agencies in the evaluation of therapies for a disease which, in spite of advances in therapy, still has a high mortality.     

Finding Jack Michael’s Footprints in the Sand

Jack Michael left a legacy of fine discriminations among technical terms, a careful parsing of theoretical concepts, and a variety of behavioral interpretations of complex behavioral phenomena. When pushing into relatively unfamiliar territory in areas such as “memory,” automatic reinforcement, multiple control, and additivity of response strength, I have been surprised and delighted to find evidence that Jack had once explored the same topics, in the same way, and had come to the same conclusions toward which I was groping.     

Residual plots for linear regression models with censored outcome data: A refined method for visualizing residual uncertainty

Residual plots are a standard tool for assessing model fit. When some outcome data are censored, standard residual plots become less appropriate. Here, we develop a new procedure for producing residual plots for linear regression models where some or all of the outcome data are censored. We implement two approaches for incorporating parameter uncertainty. We illustrate our methodology by examining the model fit for an analysis of bacterial load data from a trial for chronic obstructive pulmonary disease. Simulated datasets show that the method can be used when the outcome data consist of a variety of types of censoring.     

A predictive leverage statistic for quantile regression with measurement errors

Application of quantile regression models with measurement errors in predictors is becoming increasingly popular. High leverage points in predictors can have substantial impacts on these models. Here, we propose a predictive leverage statistic for these models, assuming that the measurement errors follow a multivariate normal distribution, and derive its exact distribution. We compare its performance versus known predictive leverage statistics using simulation and a real dataset. The proposed statistic is shown to have desirable features. It is also the first predictive leverage statistic having its distribution derived in a closed form.     

Adaptive procedure for generalized familywise error rate control

This article considers multiple hypotheses testing with the generalized familywise error rate k-FWER control, which is the probability of at least k false rejections. We first assume the p-values corresponding to the true null hypotheses are independent, and propose adaptive generalized Bonferroni procedure with k-FWER control based on the estimation of the number of true null hypotheses. Then, we assume the p-values are dependent, satisfying block dependence, and propose adaptive procedure with k-FWER control. Extensive simulations compare the performance of the adaptive procedures with different estimators.     

Exact inference for exponential distribution with multiply Type-I censored data

In this paper, we focus on exact inference for exponential distribution under multiple Type-I censoring, which is a general form of Type-I censoring and represents that the units are terminated at different times. The maximum likelihood estimate of mean parameter is calculated. Further, the distribution of maximum likelihood estimate is derived and it yields an exact lower confidence limit for the mean parameter. Based on a simulation study, we conclude that the exact limit outperforms the bootstrap limit in terms of the coverage probability and average limit. Finally, a real dataset is analyzed for illustration.