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

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Listed:
  • Marco Riani

    (University of Parma)

  • Anthony C. Atkinson

    (The London School of Economics)

  • Aldo Corbellini

    (University of Parma)

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

  • Marco Riani & Anthony C. Atkinson & Aldo Corbellini, 2023. "Automatic robust Box–Cox and extended Yeo–Johnson transformations in regression," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(1), pages 75-102, March.
    • Handle: RePEc:spr:stmapp:v:32:y:2023:i:1:d:10.1007_s10260-022-00640-7
    DOI: 10.1007/s10260-022-00640-7
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    References listed on IDEAS

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    1. Riani, Marco & Atkinson, Anthony Curtis & Corbellini, Aldo & Farcomeni, Alessio & Laurini, Fabrizio, 2024. "Information Criteria for Outlier Detection Avoiding Arbitrary Significance Levels," Econometrics and Statistics, Elsevier, vol. 29(C), pages 189-205.
    2. Tommaso Proietti & Marco Riani, 2009. "Transformations and seasonal adjustment," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(1), pages 47-69, January.
    3. Domenico Perrotta & Marco Riani & Francesca Torti, 2009. "New robust dynamic plots for regression mixture detection," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 3(3), pages 263-279, December.
    4. Marazzi, Alfio & Villar, Ana J. & Yohai, Victor J., 2009. "Robust Response Transformations Based on Optimal Prediction," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 360-370.
    5. Neykov, N. & Filzmoser, P. & Dimova, R. & Neytchev, P., 2007. "Robust fitting of mixtures using the trimmed likelihood estimator," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 299-308, September.
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    More about this item

    Keywords

    Bayesian information criterion (BIC); Constructed variable; Extended coefficient of determination $$(R^{2})$$ ( R 2 ); Forward search; Negative observations; Simultaneous test;
    All these keywords.

    JEL classification:

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

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