Suppose a linear model for Y in a single predictor var, X. If the residuals show a pattern of increasing variance (wrt X), sometimes a transformation of Y, Y'=f(Y) is considered (where f is sq rt, log, etc), which we can express in the general form Y' = Y$^\alpha$, for $\alpha \in (0,1)$
My question is the following: has anyone ever researched the method for finding the best value of the parameter $\alpha$?
I don't see many references to this topic in my texts, yet it seems like such a simple question, that someone must have worked on it. Any references or something to point me in the right direction would be greatly appreciated.