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The analysis of transformations for profit‐and‐loss data

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  • Anthony C. Atkinson
  • Marco Riani
  • Aldo Corbellini

Abstract

We analyse data on the performance of investment funds, 99 out of 309 of which report a loss, and on the profitability of 1405 firms, 407 of which report losses. The problem in both cases is to use regression to predict performance from sets of explanatory variables. In one case, it is clear from scatter plots of the data that the negative responses have a lower variance than the positive responses and a different relationship with the explanatory variables. Because the data include negative responses, the Box–Cox transformation cannot be used. We develop a robust version of an extension to the Yeo–Johnson transformation which allows different transformations for positive and negative responses. Tests and graphical methods from our robust analysis enable the detection of outliers, the assessment of values of the two transformation parameters and the building of simple regression models. Performance comparisons are made with non‐parametric transformations.

Suggested Citation

  • Anthony C. Atkinson & Marco Riani & Aldo Corbellini, 2020. "The analysis of transformations for profit‐and‐loss data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(2), pages 251-275, April.
    • Handle: RePEc:bla:jorssc:v:69:y:2020:i:2:p:251-275
    DOI: 10.1111/rssc.12389
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    References listed on IDEAS

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    1. Anthony C. Atkinson, 2002. "Forward search added-variable t-tests and the effect of masked outliers on model selection," Biometrika, Biometrika Trust, vol. 89(4), pages 939-946, December.
    2. Eleonora Bartoloni, 2013. "Profitability and innovation: new empirical findings based on italian data 1996-2003," Rivista Internazionale di Scienze Sociali, Vita e Pensiero, Pubblicazioni dell'Universita' Cattolica del Sacro Cuore, vol. 121(2), pages 137-170.
    3. 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.
    4. Marco Riani & Anthony C. Atkinson & Andrea Cerioli, 2009. "Finding an unknown number of multivariate outliers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 447-466, April.
    5. Joe Whittaker & Chris Whitehead & Mark Somers, 2005. "The neglog transformation and quantile regression for the analysis of a large credit scoring database," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(5), pages 863-878, November.
    6. Eleonora Bartoloni, 2013. "Profitability and innovation: new empirical findings based on italian data 1996-2003," Rivista Internazionale di Scienze Sociali, Vita e Pensiero, Pubblicazioni dell'Universita' Cattolica del Sacro Cuore, vol. 122(2), pages 137-170.
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    Cited by:

    1. Francesca Torti & Aldo Corbellini & Anthony C. Atkinson, 2021. "fsdaSAS: A Package for Robust Regression for Very Large Datasets Including the Batch Forward Search," Stats, MDPI, vol. 4(2), pages 1-21, April.
    2. Torti, Francesca & Corbellini, Aldo & Atkinson, Anthony C., 2021. "fsdaSAS: a package for robust regression for very large datasets including the batch forward search," LSE Research Online Documents on Economics 109895, London School of Economics and Political Science, LSE Library.
    3. Atkinson, Anthony C. & Riani, Marco & Corbellini, Aldo, 2021. "The box-cox transformation: review and extensions," LSE Research Online Documents on Economics 103537, London School of Economics and Political Science, LSE Library.
    4. 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.

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

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