The Box-Cox family of power transformations (Box and Cox 1964) is defined by

where λ is a free parameter.
(a) Show that, for each y, g*λ(y) is continuous in A. In particular, show that

(b) Find the function v(θ), the approximate variance of Y, that g*λ(y) stabilizes. (v(θ) will most likely also depend on λ.)
Analysis of transformed data in general and the Box-Cox power transformation in particular has been the topic of some controversy in the statistical literature. See Bickel and Doksum (1981), Box and Cox (1982), and Hinkley and Runger (1984).

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if λ , log y limów"-1)/λ = logy.