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Box‐Cox transformed linear models: A parameter‐based asymptotic approach
Author(s) -
Chen Gemai,
Lockhart Richard A.
Publication year - 1997
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 - 10.2307/3315345
Subject(s) - frequentist inference , power transform , inference , mathematics , linear model , inverse , proportional hazards model , statistics , bayesian inference , discrete mathematics , bayesian probability , computer science , artificial intelligence , geometry , consistency (knowledge bases)
A Box‐Cox transformed linear model usually has the form y (λ) = μ + β 1 x 1 +… + β p x p + oe, where y (λ) is the power transform of y. Although widely used in practice, the Fisher information matrix for the unknown parameters and, in particular, its inverse have not been studied seriously in the literature. We obtain those two important matrices to put the Box‐Cox transformed linear model on a firmer ground. The question of how to make inference on β = (β 1 ,…,β p ) T when λ; is estimated from the data is then discussed for large but finite sample size by studying some parameter‐based asymptotics. Both unconditional and conditional inference are studied from the frequentist point of view.