Tail behavior of the least-squares estimator

Jana Jurečková, Roger Koenker, Stephen Portnoy

Research output: Contribution to journalArticle

Abstract

The tail behavior of the least-squares estimator in the linear regression model was studied in He et al. (Econometrica 58 (1990) 1195) under a fixed design for finite n. We now consider a random design matrix Xn and the case n→∞ and study the probability P0(max1≤i≤n|xi′β̂ n|≥γn) with γn=F-1(1-1/n), a population analog of the maximal error. Unlike in the situation with fixed n and γ→∞, for n→∞ we find fairly good tail behavior of LSE for normal F, for both fixed and random designs, even under heavy-tailed distribution for Xn.

Original languageEnglish (US)
Pages (from-to)377-384
Number of pages8
JournalStatistics and Probability Letters
Volume55
Issue number4
DOIs
StatePublished - Dec 15 2001

Keywords

  • Domain of attraction
  • Extreme values
  • Least-squares estimator
  • Tail behavior

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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