Efficient and adaptive rank-based fits for linear models with skew-normal errors

Abstract

The rank-based fit of a linear model is based on minimizing a norm. A score function needs to be selected for the fit and the proper choice leads to asymptotically efficient regression estimators, i.e., fits equivalent to the maximum likelihood estimators (mle). In this paper, we present the family of optimal scores functions for the skew-normal family of distributions. We show the easy computation of this rank-based fit using the R package Rfit. We present the results of a small simulation study comparing the rank-based estimators and the mles in terms of efficiency and validity over skew-normal and contaminated normal distributions. We also develop and present empirical results for a Hogg-type adaptive procedure for selecting among a family of these scores based on a robust initial fit.