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

Author

Zhenlin YANG, Singapore Management UniversityFollow

Publication Type

Journal Article

Version

publishedVersion

Publication Date

6-1999

Abstract

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.

Keywords

Asymptotic expansion, Box-Cox transformation, sensitivity, T-ratio, lambda-fixed

Discipline

Econometrics

Research Areas

Econometrics

Publication

TEST

Volume

8

Issue

1

First Page

167

Last Page

190

ISSN

1133-0686

Identifier

10.1007/BF02595868

Citation

YANG, Zhenlin. Estimating a transformation and its effect on Box-Cox T-ratio. (1999). TEST. 8, (1), 167-190.
Available at: https://ink.library.smu.edu.sg/soe_research/2152

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.

Additional URL

https://doi.org/10.1007/BF02595868