The Annals of Statistics

Direct use of regression quantiles to construct confidence sets in linear models

Stephen L. Portnoy and Kenneth Q. Zhou

Full-text: Open access

Abstract

Direct use of the empirical quantile function provides a standard distribution-free approach to constructing confidence intervals and confidence bands for population quantiles. We apply this method to construct confidence intervals and confidence bands for regression quantiles and to construct prediction intervals based on sample regression quantiles. Comparison of the direct method with the studentization and the bootstrap methods are discussed. Simulation results show that the direct method has the advantage of robustness against departure from the normality assumption of the error terms.

Article information

Source
Ann. Statist., Volume 24, Number 1 (1996), 287-306.

Dates
First available in Project Euclid: 26 September 2002

Permanent link to this document
https://projecteuclid.org/euclid.aos/1033066210

Digital Object Identifier
doi:10.1214/aos/1033066210

Mathematical Reviews number (MathSciNet)
MR1389891

Zentralblatt MATH identifier
0853.62040

Subjects
Primary: 62G15: Tolerance and confidence regions 62E20: Asymptotic distribution theory 62J05: Linear regression

Keywords
Conditional quantiles Bahadur representation confidence intervals confidence bands empirical levels Brownian bridge

Citation

Zhou, Kenneth Q.; Portnoy, Stephen L. Direct use of regression quantiles to construct confidence sets in linear models. Ann. Statist. 24 (1996), no. 1, 287--306. doi:10.1214/aos/1033066210. https://projecteuclid.org/euclid.aos/1033066210


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