Strong consistency of regression quantiles and related empirical processes

Gilbert W. Bassett, Roger W. Koenker

Research output: Contribution to journalArticlepeer-review

Abstract

The strong consistency of regression quantile statistics (Koenker and Bassett [4]) in linear models with iid errors is established. Mild regularity conditions on the regression design sequence and the error distribution are required. Strong consistency of the associated empirical quantile process (introduced in Bassett and Koenker [1]) is also established under analogous conditions. However, for the proposed estimate of the conditional distribution function of Y, no regularity conditions on the error distribution are required for uniform strong convergence, thus establishing a Glivenko-Cantelli-type theorem for this estimator.

Original languageEnglish (US)
Pages (from-to)191-201
Number of pages11
JournalEconometric Theory
Volume2
Issue number2
DOIs
StatePublished - Aug 1986

ASJC Scopus subject areas

  • Social Sciences (miscellaneous)
  • Economics and Econometrics

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