Rank estimation of regression coefficients using iterated reweighted least squares

This paper is concerned with the rank estimator for the parameter vector β in a linear model which is obtained by the minimization of a rank dispersion function. The rank estimator has many advantages over the regular least squares estimator, but the inaccessibility of software to carry out its computation has limited its use. An iterated reweighted least squares algorithm is presented for the computation of the rank estimator. The method is simple in concept and can be carried out readily with a wide variety of statistical software. Details of the method are discussed along with some results on its asymptotic distribution and numerical stability. Some examples are presented to show advantages of the rank method.