L-ESTIMATION OF THE PARAMETERS IN A LINEAR MODEL BASED ON A FEW SELECTED REGRESSION QUANTILES

Abstract

This paper considers the L-estimation of regression and scale parameter of the linear model
Y = 01o + X + e, where 0 is the intercept parameters and is the scale in the
model, based on k( n) optimum regression quantiles as defined by Koenker and Bassett
(1978). In addition, the paper contains the trimmed estimation problem with continuous
weight functions, the estimation of conditional regression function and the related optimum
regression quantiles.