Estimating a transformation and its effect on Box-CoxT-ratio

• Published in: Test (Madrid, Spain) Spain), 1999-06, Vol.8 (1), p.167-190
• Main Author: Yang, Zhelin
• Format: Article
• Language: English
• Subjects: Monte Carlo simulation; Studies
• ISSN: 1133-0686; 1863-8260
• DOI: 10.1007/BF02595868

This article concernsi) the stochastic behavior of the Box-Cox transformation estimator andii) 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 σ^sub 0^. 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 σ^sub 0^ are both small; and a one-mean mode can give a poor-estimate if σ^sub 0^ is small. When the sample is not large, it is shown that the unconditional effect of estimating a transformation on the Box-CoxT-ratio is generally small, and the "conditional" effect is also negligible in most of the situations except the case of one-way ANOVA with small σ^sub 0^. Extensive Monte Carlo simulations are performed to support the theoretical findings.[PUBLICATION ABSTRACT]