Some pathological regression asymptotics under stable conditions
type: Item
instance of: scholarly article
title: Some pathological regression asymptotics under stable conditions
zbMATH Open document ID: 1103.62354
DOI: 10.1016/S0167-7152(00)00107-3
published in: Statistics \& Probability Letters
publication date: 2000-01-01T00:00:00Z
review text: We consider a simple through-the-origin linear regression example introduced by P. J. Rousseeuw, S. van Aelst and M. Hubert. It is shown that the conventional least squares and least absolute error estimators converge in distribution without normalization and consequently are inconsistent. A class of weighted median regression estimators, including the maximum depth estimator of Rousseeuw and Hubert [\textit{P. J. Rousseeuw} and \textit{M. Hubert}, J. Am. Stat. Assoc. 94, No. 446, 388--433 (1999; Zbl 1007.62060)], are shown to converge at rate \(n^{-1}\). Finally, the maximum likelihood estimator is considered, and we observe that there exist estimators that converge at rate \(n^{-2}\). The results illustrate some interesting, albeit somewhat pathological, aspects of stable-law convergence.
Mathematics Subject Classification ID: 62J05
Mathematics Subject Classification ID: 62F12
zbMATH DE Number: 1546526
zbMATH Keywords: Asymptotics
zbMATH Keywords: Median regression
zbMATH Keywords: LAD regression
zbMATH Keywords: Stable law
zbMATH Keywords: Data depth
author: Roger Koenker
author: Stephen Portnoy
MaRDI profile type: Publication
cites work: A Method for Simulating Stable Random Variables
cites work: Q4695322
cites work: Q4171432
cites work: Regression Quantiles
cites work: A study of logspline density estimation
cites work: Parameterizations and modes of stable distributions
cites work: Regression Depth
cites work: Q5610809
cites work: On the Chambers-Mallows-Stuck method for simulating skewed stable random variables
cites work: Q3673748
description: scientific article; zbMATH DE number 1546526