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Forward search added-variable t-tests and the effect of masked outliers on model selection

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  • Anthony C. Atkinson

Abstract

Monitoring the t-tests for individual regression coefficients in 'forward' search fails to identify the importance of observations to the significance of the individual regressors. This failure is due to the ordering of the data by the search. We introduce an added-variable test which has the desired properties since the projection leading to residuals destroys the effect of the ordering. An example illustrates the effect of several masked outliers on model selection. Comments are given on the related test for response transformations. Copyright Biometrika Trust 2002, Oxford University Press.

Suggested Citation

  • 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.
    • Handle: RePEc:oup:biomet:v:89:y:2002:i:4:p:939-946
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    Citations

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    Cited by:

    1. 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.
    2. Riani, Marco & Atkinson, Anthony C., 2010. "Robust model selection with flexible trimming," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3300-3312, December.
    3. Menjoge, Rajiv S. & Welsch, Roy E., 2010. "A diagnostic method for simultaneous feature selection and outlier identification in linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3181-3193, December.
    4. Anthony Atkinson, 2009. "Econometric Applications of the Forward Search in Regression: Robustness, Diagnostics, and Graphics," Econometric Reviews, Taylor & Francis Journals, vol. 28(1-3), pages 21-39.
    5. Cerioli, Andrea & Farcomeni, Alessio & Riani, Marco, 2014. "Strong consistency and robustness of the Forward Search estimator of multivariate location and scatter," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 167-183.
    6. Daniele Coin, 2008. "Testing normality in the presence of outliers," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 17(1), pages 3-12, February.
    7. De Bin, Riccardo & Boulesteix, Anne-Laure & Sauerbrei, Willi, 2017. "Detection of influential points as a byproduct of resampling-based variable selection procedures," Computational Statistics & Data Analysis, Elsevier, vol. 116(C), pages 19-31.
    8. 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.
    9. Jurgen A. Doornik & David F. Hendry, 2016. "Outliers and Model Selection: Discussion of the Paper by Søren Johansen and Bent Nielsen," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 360-365, June.
    10. Andreas Alfons & Wolfgang Baaske & Peter Filzmoser & Wolfgang Mader & Roland Wieser, 2011. "Robust variable selection with application to quality of life research," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 20(1), pages 65-82, March.
    11. Riani Marco, 2004. "Extensions of the Forward Search to Time Series," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-25, May.
    12. Sung-Soo Kim & Sung Park & W. J. Krzanowski, 2008. "Simultaneous variable selection and outlier identification in linear regression using the mean-shift outlier model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(3), pages 283-291.

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