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Regression Rank Scores and Regression Quantiles

1992; Institute of Mathematical Statistics; Volume: 20; Issue: 1 Linguagem: Inglês

10.1214/aos/1176348524

2168-8966

Christoph Gutenbrünner, Jana Jurečková,

Statistical Methods and Inference

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.