Strong Consistency of Regression Quantiles and Related Empirical Processes
- 1 April 1986
- journal article
- research article
- Published by Cambridge University Press (CUP) in Econometric Theory
- Vol. 2 (2) , 191-201
- https://doi.org/10.1017/s0266466600011488
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.Keywords
This publication has 8 references indexed in Scilit:
- Four (Pathological) Examples in Asymptotic StatisticsThe American Statistician, 1984
- Four (Pathological) Examples in Asymptotic StatisticsThe American Statistician, 1984
- An Empirical Quantile Function for Linear Models with | operatornameiid ErrorsJournal of the American Statistical Association, 1982
- An Empirical Quantile Function for Linear Models with iid ErrorsJournal of the American Statistical Association, 1982
- Robust Tests for Heteroscedasticity Based on Regression QuantilesEconometrica, 1982
- Some Large-Sample Tests for Nonnormality in the Linear Regression Model: CommentJournal of the American Statistical Association, 1980
- Regression QuantilesEconometrica, 1978
- Convex AnalysisPublished by Walter de Gruyter GmbH ,1970