Asymptotic theory for Box–Cox transformations in linear models

We investigate large sample properties of the Box–Cox estimators when the Box–Cox transformed responses follow a regression model. We first extend Rubin's [Ann. Math. Statist. 27 (1956) 200–203] theorem and then establish the strong consistency and asymptotic normality of the Box–Cox estimators...

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Bibliographic Details
Published in:Statistics & probability letters 2001-02, Vol.51 (4), p.337-343
Main Authors: Cho, Kwanho, Yeo, In-Kwon, Johnson, Richard A., Loh, Wei-Yin
Format: Article
Language:English
Subjects:
Asymptotic normality
Consistency
Distribution theory
Exact sciences and technology
Linear inference, regression
Mathematics
Nonparametric inference
Probability and statistics
Sciences and techniques of general use
Statistics
Transformation
Transformation Consistency Asymptotic normality Uniform convergence
Uniform convergence
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Summary:We investigate large sample properties of the Box–Cox estimators when the Box–Cox transformed responses follow a regression model. We first extend Rubin's [Ann. Math. Statist. 27 (1956) 200–203] theorem and then establish the strong consistency and asymptotic normality of the Box–Cox estimators.
ISSN:0167-7152
1879-2103
DOI:10.1016/S0167-7152(00)00170-X