The Annals of Statistics

Regression Rank Scores and Regression Quantiles

C. Gutenbrunner and J. Jureckova

Full-text: Open access

Abstract

We show that regression quantiles, which could be computed as solutions of a linear programming problem, and the solutions of the corresponding dual problem, which we call the regression rank-scores, generalize the duality of order statistics and of ranks from the location to the linear model. Noting this fact, we study the regression quantile and regression rank-score processes in the heteroscedastic linear regression model, obtaining some new estimators and interesting comparisons with existing estimators.

Article information

Source
Ann. Statist. Volume 20, Number 1 (1992), 305-330.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176348524

Digital Object Identifier
doi:10.1214/aos/1176348524

Mathematical Reviews number (MathSciNet)
MR1150346

Zentralblatt MATH identifier
0759.62015

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62J05: Linear regression

Keywords
Regression quantile regression rank-score trimmed least-squares estimator $L$-statistic linear rank statistic

Citation

Gutenbrunner, C.; Jureckova, J. Regression Rank Scores and Regression Quantiles. Ann. Statist. 20 (1992), no. 1, 305--330. doi:10.1214/aos/1176348524. https://projecteuclid.org/euclid.aos/1176348524


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