COMPUTATIONAL ASPECTS OF ADAPTIVE COMBINATION OF LEAST-SQUARES AND LEAST ABSOLUTE DEVIATIONS ESTIMATORS

Dodge and Jureckova (1987) showed that the estimation of linear regression parameter vector by a convex combination of least squares and least absolute deviation estimators could be adapted so that the resulting estimator achieves the minimum asymptotic variance in the model under consideration. The present paper considers the computational aspects of this adaptive estimator; an algorithm based on the iteratively reweighted least squares method is recommended and formally described. Technical details and an effect of the choice of a normalizing constant, appearing in the definition of the estimator, are also discussed. The behavior of the procedure is demonstrated on example.