The QUANTSELECT Procedure

Quantile Regression

Subsections:

This section describes the basic concepts and notations for quantile regression and quantile regression model selection.

Let denote a data set of observations, where are responses, and are regressors. Koenker and Bassett (1978) defined the regression quantile at quantile level as any solution that minimizes the following objective function in :

where is a check loss function in which and .

If you specify weights , in the WEIGHT statement, weighted quantile regression is carried out by solving