Score test in robust M-procedure

Abstract

A score type test based on the M-estimation method for a linear regression model is more reliable than the parametric based-test under mild departures from model assumptions, or when dataset has outliers. An R-function is developed for the score M-test, and applied to two real datasets to illustrate the procedure. The asymptotic power function of the M-test under a sequence of (contiguous) local alternatives is derived. Through computation of power function from simulated data, the M-test is compared with its alternatives, the Student's $t$ and Wilcoxon's rank tests. Graphical illustration of the asymptotic power of the M-test is provided for randomly generated data from the normal, Laplace, Cauchy, and logistic distributions