ROBUST INFERENCE IN PARAMETRIC MODELS USING THE FAMILY OF GENERALIZED NEGATIVE EXPONENTIAL DISPARITIES

We examine robust estimators and tests using the family of generalized negative exponential disparities, which contains the Pearson's chi‐square and the ordinary negative exponential disparity as special cases. The influence function and α‐influence function of the proposed estimators are discussed and their breakdown points derived. Under the model, the estimators are asymptotically efficient, and are shown to have an asymptotic breakdown point of 50%. The proposed tests are shown to be equivalent to the likelihood ratio test under the null hypothesis, and their breakdown points are obtained. The competitive performance of the proposed estimators and tests relative to those based on the Hellinger distance is illustrated through examples and simulation results. Unlike the Hellinger distance, several members of this family of generalized negative exponential disparities generate estimators which also possess excellent inlier‐controlling capability. The corresponding tests of hypothesis are shown to have better power breakdown than the Hellinger deviance test in the cases examined.     

USE OF A LOG-LINEAR MODEL TO COMPUTE THE EMPIRICAL SURVIVAL CURVE FROM INTERVAL-CENSORED DATA, WITH APPLICATION TO DATA ON TESTS FOR HIV POSITIVITY

We describe how a log-linear model can be used to compute the nonparametric maximum likelihood estimate of the survival curve from interval-censored data. This permits such computation to be performed with the aid of readily available statistical software such as GLIM or SAS. The method is illustrated with reference to data from a cohort of Danish homosexual men, each of whom was tested for HIV positivity on one or more of six possible follow-up times.     

INFLUENTIAL OBSERVATION IDENTIFICATION IN THE GROWTH CURVE MODEL WITH RAO'S SIMPLE COVARIANCE STRUCTURE

ABSTRACT

In this paper we discuss the identification of influential observations in a growth curve model with Rao's simple covariance structure. Based on the generalized Cook-type distance and the volume of a confidence ellipsoid, a variety of influence measures are proposed in terms of the case-deletion technique. Also, the influence of observations on a linear combination of regression coefficients is considered. For illustration, a practical example is analyzed using the proposed approach.     

AN ALGORITHMIC APPROACH TO BAYESIAN LINEAR MODEL CALCULATIONS

A framework is described for organizing and understanding the computations necessary to obtain the posterior mean of a vector of linear effects in a normal linear model, conditional on the parameters that determine covariance structure. The approach has two major uses; firstly, as a pedagogical tool in the derivation of formulae, and secondly, as a practical tool for developing computational strategies without needing complicated matrix formulae that are often unwieldy in complex hierarchical models. The proposed technique is based upon symbolic application of the sweep operator SWP to an appropriate tableau of means and covariances. The method is illustrated with standard linear model specifications, including the so-called mixed model, with both fixed and random effects.     

SIMULTANEOUS CONFIDENCE REGIONS IN AN EXTENDED GROWTH CURVE MODEL WITH k HIERARCHICAL WITHIN-INDIVIDUALS DESIGN MATRICES

ABSTRACT

We consider an extended growth curve model with k hierarchical within-individuals design matrices. The model includes the one whose mean structure consists of polynomial growth curves with k different degrees. First we propose certain simple estimators of the mean and covariance parameters which are closely related to the MLE's. Using these estimators we construct simultaneous confidence regions for each or all of k growth curves which is an extension of Fujikoshi.[2] Fujikoshi, Y. 1999. Simultaneous Confidence Intervals in an Extended Growth Curves. Commun. Statist.–-Theor. Meth., 28: 671–682. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar] A numerical example with k = 3 is also given.     

ANALYSIS OF MASKED DATA IN A DEPENDENT COMPETING RISKS MODEL UNDER UNKNOWN ENVIRONMENT

ABSTRACT

System failure data is often analyzed to estimate component reliabilities. Due to cost and time constraints, the exact component causing the failure of the system cannot be identified in some cases. This phenomenon is called masking. Further, it is sometimes necessary for us to take account of the influence of the operating environment. Here we consider a series system, operating under unknown environment, of two components whose failure times follow the Marshall-Olkin bivariate exponential distribution. We present a maximum likelihood approach for obtaining estimators from the masked data for this system. From a simulation study, we found that the relative errors of the estimates are almost well behaved even for small or moderate expected number of systems whose cause of failure is identified.