Regression rank scores estimation in ANOCOVA
type: Item
instance of: scholarly article
title: Regression rank scores estimation in ANOCOVA
zbMATH Open document ID: 0898.62087
author: Pranab K. Sen
published in: The Annals of Statistics
publication date: 1998-11-03T00:00:00Z
review text: To motivate semiparametric analysis of covariance (ANOCOVA) models, consider first the conventional model where for the \(i\) th observation, \(Y_i\), \({\mathbf Z}_t\), and \({\mathbf t}_i\) stand for the primary, (stochastic) concomitant and (nonstochastic) design variates, respectively, and, conditional on \({\mathbf Z}_i= {\mathbf z}_i\), \[ Y_i= {\beta}'{\mathbf t}_i+ {\gamma}'{\mathbf z}_i+ e_i, \qquad i=1,\dots, n,\tag{1} \] where \({\beta}\) and \({\gamma}\) are the regression parameter vectors for the fixed and random effects components, and the \(e_i\) are independent and identically distributed random variables (i.i.d. r.v.'s) having a normal distribution with mean 0 and a finite (conditional) variance \(\sigma^2\). The \({\mathbf t}_i\) are given \(p\)-vectors not all equal, \({\mathbf T}= ({\mathbf t}_1,\dots, {\mathbf t}_n)'\) and the \({\mathbf Z}_i\) are stochastic \(q\)-vectors, so that there are \(p+q\) regression parameters and an additional scale parameter \(\sigma\). The assumed joint normality of \(({\mathbf Z}_i, e_i)\) yields homoscedasticity, linearity of regression as well as normality of the conditional distribution in (1). Without this joint normality, a breakdown may occur in each of these three basic postulations. On the other hand, the design vectors may still pertain to a linear regression function. Thus, there is a need to examine thoroughly the robustness aspects of mixed-effects models with due emphasis on all these factors. The role of regression rank scores in robust estimation of fixed-effects parameters as well as covariate regression functionals is critically appraised, and the relevant asymptotic theory is presented.
Mathematics Subject Classification ID: 62J05
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 62G20
zbMATH DE Number: 1006597
zbMATH Keywords: heteroscedasticity
zbMATH Keywords: regression quantiles
zbMATH Keywords: R-estimators
zbMATH Keywords: stochastic predictors
zbMATH Keywords: weak invariance principles
zbMATH Keywords: semiparametric analysis
zbMATH Keywords: mixed-effects models
zbMATH Keywords: regression rank scores
zbMATH Keywords: robust estimation
zbMATH Keywords: covariate regression functionals
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1032298286
OpenAlex ID: W2045941204
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DOI: 10.1214/AOS/1032298286
description: scientific article; zbMATH DE number 1006597