Computational Statlstlcs & Data Analysis 12 (1991) 87-99 North-Holland 87 Computational aspects of adaptive combination of least squares and least absolute deviations estimators Yadolah Dodge Unrversrty of NeuchZtel, 2000 Neuchitel, Swrtrerland Jarormr Antoch Charles Unrvemty, 18600 Prague 8, Czechoslovakra Jana JureEkovh Charles Umverslty, 18600 Prague 8, Czechoslovakia Received March 1989 Revised June 1990 Abstract Dodge and JureEkovi (1987) showed that the estimation of linear regression parameter vector by a convex combmatlon of least squares and least absolute devlatlon estimators could be adapted so that the resulting estimator a&eves the mmlmum asymptotic vanance m the model under conslderatlon The present paper considers the computational aspects of this adaptive estimator, an algonthm based on the iteratively reweighted least squares method 1s recommended and formally described Technical detads and an effect of the choice of a normahzmg constant, appearmg m the defmltlon of the estimator, are also discussed. The behavior of the procedure IS demonstrated on example Keywords Adaptive estimator, Least squares estimator, Least absolute devlatlons estimator, Linear regresslon model, M-estimator zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA 1. Introduction Consider the linear regression model zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHG y=xfl+z, where Y IS an (n X 1) vector of observations, X = X,, IS an (n X p) design matrix, / 3 IS a ( p x 1) vector of unknown parameters and Z IS an (n x 1) vector of independent errors, ldentlcally distributed with a symmetnc density zyxwvutsrqponmlkjihgfedcb f which IS generally unknown. 0167-9473/ 91/ $03 50 0 1991 - Elsevler Science Publishers B V (North-Holland)