Estimating a transformation and its effect on Box-Cox T-ratio

• Main Author: YANG, Zhenlin
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 1999
• Subjects: Asymptotic expansion; Box-Cox transformation; sensitivity; T-ratio; lambda-fixed; Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/2152; https://ink.library.smu.edu.sg/context/soe_research/article/3152/viewcontent/Yang_Test_Box_Cox.pdf
• Institution: Singapore Management University

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 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 σ0. Extensive Monte Carlo simulations are performed to support the theoretical findings.