Social and Behavioral Sciences Commons^™

Estimating A Transformation And Its Effect On Box-Cox T-Ratio, Zhenlin Yang

Research Collection School Of Economics

This article concerns i) the stochastic behavior of the Box-Cox transformation estimator and ii) the effect of estimating a transformation on the Box-CoxT-ratio used for the post-transformation analysis. It is shown that the transformation estimator depends on three factors: the model structure, the mean-spread and the error standard deviation σ0. In general, a structured model is able to estimate the transformation very well; an unstructured model can do well also unless the mean-spread and σ0 are both small; and a one-mean mode can give a poor-estimate if σ0 is small. When the sample is not large, it is shown that …