Why is the Box-Cox transformation so effective?

This question has intrigued my curiosity for many years.

I have had the opportunity to talk both to Box and to Cox about their transformation (Box and Cox, 1964). I conversed with the late George Box (deceased last March at age 94) when I was a visitor in Madison, Wisconsin, back in 1993-4.

A few years later I talked to David Cox at a conference on reliability in Bordeaux (MMR’2000).

I asked them both the same question, I received the same response.

The question was: What was the theory that led to the derivation of the Box-Cox transformation?

The answer was: “No theory. This was a purely empirical observation”.

The question therefore remains: Why is the Box-Cox transformation so effective, in particular when applied to a response variable in the framework of linear regression analysis?

In a new article, posted in my personal library at the American Statistical Association (ASA) site, I discuss this issue at some length. The article is now generally available for download here (Article #1 below).

Haim Shore_1_ASA_Nov 2013

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