The score statistic for regression transformation

Abstract

The score statistic for regression transformation using a parametric family is developed further; a simple formula for the approximate variance matrix of score statistics, based on asymptotic theory, is applied to yield the score statistic T S for regression transforma tion. This is compared to Atkinson's T D statistic for the same problem, and yields an improvement to its standardization. Simulations indicate that the significance levels of the proposed score statistic T S are very close to their nominal values.