The score statistic for regression transformation

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 TS for regression transforma tion. This is compared to Atkinson's TD statistic for the same problem, and yields an improvement to its standardization. Simulations indicate that the significance levels of the proposed score statistic TS are very close to their nominal values.