Author :
Alimoradi, soroush,Ehsanes Saleh, K.
Abstract :
The theory of linear combinations (L-estimation) of order statistics/sample quantiles for the location model is well-known. This paper considers the problem of L-estimation in linear models. First, we extend L-estimation methods for the regression parameters in a linear model based on a few selected regression quantiles and deal with the question of optimum regression quantiles. Second, we consider Bahadur type representation of the regression quantiles and the trimmed LSE under less restrictive conditions than that of Jureckova (1984) and we prove the asymptotic normality of these etimators. Third, we consider the estimation of the regression parameters under some uncertain prior sub-space restriction leading to the combination of two diverse areas, namely, robust estimation and shrinkage estimation via preliminary test approach.
