Abstract
Abstract We investigate the large-sample behavior of the Box-Cox procedures for selecting a transformation to normality. The study of the large-sample behavior clearly reveals the role played by the assumptions. Based on our large-sample results, we introduce an information number approach for transforming a known distribution to near normality. This latter procedure provides bench marks for the maximum amount of improvement achievable through power transformations. We illustrate our procedure with three examples. Finally, we generalize our conclusions to random vector and linear model situations.
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