The Annals of Statistics

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

Stephen L. Portnoy and Kenneth Q. Zhou

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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

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

First available in Project Euclid: 26 September 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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.

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