Adaptive LAD + TLS Regression

Abstract

The trimmed least squares estimator in the linear regression model, proposed by Koenker and Bassett in (1978), became very popular in the statistical community and among applied statisticians and econometricians. The reason for this popularity may lie in the fact that the idea behind this estimation is natural, combining concepts of the least squares and the trimmed mean, and that it could be easily computed combining a modified simplex procedure with the ordinary least squares algorithm. It is also reasonably robust against distribution outliers. Hence, it is naturally interesting to investigate a possible adaptive combination of LAD and trimmed LS estimators and in this way extend the family of estimators useful for the practice. The adaptive combination of LAD and the trimmed LS estimators was first studied by Dodge and Jurečková (1992). This adaptive estimator is the main subject of the present chapter; besides the theory, it also contains an illustrative example, which facilitates an orientation for an applied user.