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Box‐Cox transformations in linear models: Large sample theory and tests of normality
Author(s) -
Chen Gemai,
Lockhart Richard A.,
Stephens Michael A.
Publication year - 2002
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315946
Subject(s) - normality , mathematics , asymptotic distribution , estimator , statistics , inference , power transform , transformation (genetics) , residual , asymptotic analysis , linear model , normal distribution , standard error , sample (material) , statistical inference , local asymptotic normality , econometrics , computer science , algorithm , discrete mathematics , biochemistry , chemistry , consistency (knowledge bases) , chromatography , artificial intelligence , gene
The authors provide a rigorous large sample theory for linear models whose response variable has been subjected to the Box‐Cox transformation. They provide a continuous asymptotic approximation to the distribution of estimators of natural parameters of the model. They show, in particular, that the maximum likelihood estimator of the ratio of slope to residual standard deviation is consistent and relatively stable. The authors further show the importance for inference of normality of the errors and give tests for normality based on the estimated residuals. For non‐normal errors, they give adjustments to the log‐likelihood and to asymptotic standard errors.