Automatic robust Box–Cox and extended Yeo–Johnson transformations in regression

Marco Riani, Anthony C. Atkinson () and Aldo Corbellini ()
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Anthony C. Atkinson: The London School of Economics
Aldo Corbellini: University of Parma

Statistical Methods & Applications, 2023, vol. 32, issue 1, No 4, 75-102

Abstract: Abstract The paper introduces an automatic procedure for the parametric transformation of the response in regression models to approximate normality. We consider the Box–Cox transformation and its generalization to the extended Yeo–Johnson transformation which allows for both positive and negative responses. A simulation study illuminates the superior comparative properties of our automatic procedure for the Box–Cox transformation. The usefulness of our procedure is demonstrated on four sets of data, two including negative observations. An important theoretical development is an extension of the Bayesian Information Criterion (BIC) to the comparison of models following the deletion of observations, the number deleted here depending on the transformation parameter.

Keywords: Bayesian information criterion (BIC); Constructed variable; Extended coefficient of determination $$(R^{2})$$ ( R 2 ); Forward search; Negative observations; Simultaneous test (search for similar items in EconPapers)
Date: 2023
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Working Paper: Automatic robust Box-Cox and extended Yeo-Johnson transformations in regression (2023)
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DOI: 10.1007/s10260-022-00640-7

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