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Testing regression models with selection-biased data

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  • J. Ojeda
  • W. González-Manteiga
  • J. Cristóbal

Abstract

In this paper, we study integrated regression techniques to check the adequacy of a given model in the context of selection-biased observations. We introduce integrated regression in this setting, providing not only a suitable statistic for enabling a model checking test, but also a bootstrap distributional approximation to carry out the test. We also address the behaviour of the test under different alternatives showing that this behaviour is asymptotically the same for both selection-biased and non selection-biased data. The technique is illustrated with a simulation study and a data analysis based on a real situation that shows the performance of the method and how selection bias affect both estimation and inference. Copyright The Institute of Statistical Mathematics, Tokyo 2015

Suggested Citation

  • J. Ojeda & W. González-Manteiga & J. Cristóbal, 2015. "Testing regression models with selection-biased data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(3), pages 411-436, June.
    • Handle: RePEc:spr:aistmt:v:67:y:2015:i:3:p:411-436
    DOI: 10.1007/s10463-014-0463-z
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    References listed on IDEAS

    as
    1. J. Ojeda & J. Cristóbal & J. Alcalá, 2008. "A bootstrap approach to model checking for linear models under length-biased data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(3), pages 519-543, September.
    2. J. Cristóbal & J. Ojeda & J. Alcalá, 2004. "Confidence bands in nonparametric regression with length biased data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(3), pages 475-496, September.
    3. Jianqing Fan & Jiancheng Jiang, 2007. "Rejoinder on: Nonparametric inference with generalized likelihood ratio tests," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(3), pages 471-478, December.
    4. Jianqing Fan & Jiancheng Jiang, 2007. "Nonparametric inference with generalized likelihood ratio tests," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(3), pages 409-444, December.
    5. Ingrid Keilegom & Wenceslao González Manteiga & César Sánchez Sellero, 2008. "Goodness-of-fit tests in parametric regression based on the estimation of the error distribution," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 17(2), pages 401-415, August.
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