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Strong Consistency of Regression Quantiles and Related Empirical Processes

Published online by Cambridge University Press:  18 October 2010

Gilbert W. Bassett  and
Roger W. Koenker
Gilbert W. Bassett
Affiliation:
University of Illinois at Chicago
Roger W. Koenker
Affiliation:
University of Illinois at Champaign–Urbana
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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.

Type
Articles
Information
Econometric Theory , Volume 2 , Issue 2 , August 1986 , pp. 191 - 201
Copyright
Copyright © Cambridge University Press 1986

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References

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