A new class of score generating functions for regression models

In this paper we introduce a new score generating function for the rank dispersion function in a multiple linear regression model. The score function compares the rth and sth power of the tail probabilities of the underlying probability model. We show that the rank estimator of the regression parameter based on the proposed score function converges asymptotically to a multivariate normal distribution. Further, we discuss the selection of the appropriate r and s to improve the efficiency of the rank estimate of the regression parameter. It is shown that for right- (left-) skewed distributions the values of r<s (s<r) provide higher efficiency than the Wilcoxon scores.