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Model selection in regression based on pre-smoothing

Author

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  • Marc Aerts
  • Niel Hens
  • Jeffrey Simonoff

Abstract

In this paper, we investigate the effect of pre-smoothing on model selection. Christobal et al 6 showed the beneficial effect of pre-smoothing on estimating the parameters in a linear regression model. Here, in a regression setting, we show that smoothing the response data prior to model selection by Akaike's information criterion can lead to an improved selection procedure. The bootstrap is used to control the magnitude of the random error structure in the smoothed data. The effect of pre-smoothing on model selection is shown in simulations. The method is illustrated in a variety of settings, including the selection of the best fractional polynomial in a generalized linear model.

Suggested Citation

  • Marc Aerts & Niel Hens & Jeffrey Simonoff, 2010. "Model selection in regression based on pre-smoothing," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(9), pages 1455-1472.
    • Handle: RePEc:taf:japsta:v:37:y:2010:i:9:p:1455-1472
    DOI: 10.1080/02664760903046086
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    References listed on IDEAS

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    1. 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.
    2. Patrick Royston & Douglas G. Altman, 1994. "Regression Using Fractional Polynomials of Continuous Covariates: Parsimonious Parametric Modelling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(3), pages 429-453, September.
    3. Wei Pan, 2001. "Model Selection in Estimating Equations," Biometrics, The International Biometric Society, vol. 57(2), pages 529-534, June.
    4. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, October.
    5. Wei Pan, 2001. "Akaike's Information Criterion in Generalized Estimating Equations," Biometrics, The International Biometric Society, vol. 57(1), pages 120-125, March.
    6. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    7. Hoeting, Jennifer & Raftery, Adrian E. & Madigan, David, 1996. "A method for simultaneous variable selection and outlier identification in linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 22(3), pages 251-270, July.
    8. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, October.
    9. Clifford M. Hurvich & Jeffrey S. Simonoff & Chih‐Ling Tsai, 1998. "Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(2), pages 271-293.
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