Rank-Based Estimation and Associated Inferences for Linear Models With Cluster Correlated Errors

Abstract

R estimators based on the joint ranks (JR) of all the residuals have been developed over the last 20 years for fitting linear models with independently distributed errors. In this article, we extend these estimators to estimating the fixed effects in a linear model with cluster correlated continuous error distributions for general score functions. We discuss the asymptotic theory of the estimators and standard errors of the estimators. For the related mixed model with a single random effect, we discuss robust estimators of the variance components. These are used to obtain Studentized residuals for the JR fit. A real example is discussed, which illustrates the efficiency of the JR analysis over the traditional analysis and the efficiency of a prudent choice of a score function. Simulation studies over situations similar to the example confirm the validity and efficiency of the analysis.