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

Author

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  • Riani, Marco
  • Atkinson, Anthony C.
  • Corbellini, Aldo

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.

Suggested Citation

  • Riani, Marco & Atkinson, Anthony C. & Corbellini, Aldo, 2023. "Automatic robust Box-Cox and extended Yeo-Johnson transformations in regression," LSE Research Online Documents on Economics 114903, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:114903
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    File URL: https://researchonline.lse.ac.uk/id/eprint/114903/
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    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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