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On the Estimation of the Joint Distribution in Regression Models with Censored Responses

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  • Olivier Lopez

    (Crest)

Abstract

In a regression model with univariate censored responses, a new estimatorof the joint distribution function of the covariates and response is proposed,under the assumption that the response and the censoring variable are independentconditionally to the covariates. This estimator is an extension of themultivariate empirical function used in the uncensored case. Furthermore,under some simple additional identifiability assumption, this estimator is notsensible to the "curse of dimensionality", so that it allows to infer on modelswith multidimensional covariates. Integrals with respect to this empiricalmeasure are considered. Consistency and asymptotic normality of these integralsover a class of functions is obtained, by deriving asymptotic i.i.d.representations. Several applications of the new estimator are proposed.

Suggested Citation

  • Olivier Lopez, 2007. "On the Estimation of the Joint Distribution in Regression Models with Censored Responses," Working Papers 2007-11, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2007-11
    as

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    References listed on IDEAS

    as
    1. Satten G. A. & Datta S., 2001. "The Kaplan-Meier Estimator as an Inverse-Probability-of-Censoring Weighted Average," The American Statistician, American Statistical Association, vol. 55, pages 207-210, August.
    2. César Sánchez Sellero & Wenceslao González Manteiga & Ingrid Van Keilegom, 2005. "Uniform Representation of Product‐Limit Integrals with Applications," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(4), pages 563-581, December.
    3. Ingrid Van Keilegom & Noël Veraverbeke, 1997. "Estimation and Bootstrap with Censored Data in Fixed Design Nonparametric Regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(3), pages 467-491, September.
    4. 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.
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