Regression Rank Scores and Regression Quantiles
The Annals of Statistics · 1992 · Volume 20 · Issue 1
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.
Keywords
$L$-statistic; 62G05; 62J05; Linear rank statistic; regression quantile; regression rank-score; trimmed least-squares estimator;
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