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Goodness-of-fit tests for censored regression based on artificial data points

Author

Listed:
  • Wenceslao González Manteiga

    (Universidade de Santiago de Compostela)

  • Cédric Heuchenne

    (HEC Liège, University of Liège
    Université catholique de Louvain)

  • César Sánchez Sellero

    (Universidade de Santiago de Compostela)

  • Alessandro Beretta

    (HEC Liège, University of Liège)

Abstract

Suppose we have a location-scale regression model where the location is the conditional mean and the scale is the conditional standard deviation; the response is possibly right-censored, the covariate is fully observed, and the error is independent of the covariate. We propose new goodness-of-fit testing procedures for the conditional mean and variance based on an integrated regression function technique which uses artificial data points. We obtain the weak convergence of the resulting processes and study their finite sample behavior via simulations. Finally, we analyze a data set about unemployment in Galicia.

Suggested Citation

  • Wenceslao González Manteiga & Cédric Heuchenne & César Sánchez Sellero & Alessandro Beretta, 2020. "Goodness-of-fit tests for censored regression based on artificial data points," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 599-615, June.
    • Handle: RePEc:spr:testjl:v:29:y:2020:i:2:d:10.1007_s11749-019-00662-6
    DOI: 10.1007/s11749-019-00662-6
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    References listed on IDEAS

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    1. Stute, W., 1993. "Consistent Estimation Under Random Censorship When Covariables Are Present," Journal of Multivariate Analysis, Elsevier, vol. 45(1), pages 89-103, April.
    2. Cédric Heuchenne & Ingrid Keilegom, 2010. "Estimation in nonparametric location-scale regression models with censored data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(3), pages 439-463, June.
    3. Heuchenne, Cedric & Van Keilegom, Ingrid, 2012. "Estimation of a general parametric location in censored regression," LIDAM Reprints ISBA 2012014, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Holger Dette & Cedric Heuchenne, 2012. "Scale Checks in Censored Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(2), pages 323-339, June.
    5. Cédric Heuchenne & Ingrid Keilegom, 2007. "Polynomial Regression with Censored Data based on Preliminary Nonparametric Estimation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(2), pages 273-297, June.
    6. Heuchenne, C. & Van Keilegom, I., 2010. "Estimation in nonparametric location-scale regression models with censored data," LIDAM Reprints ISBA 2010015, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Heuchenne, Cedric & Laurent, Geraldine, 2017. "Parametric conditional variance estimation in location-scale models with censored data," LIDAM Reprints ISBA 2017012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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