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The copula-graphic estimator in censored nonparametric location-scale regression models

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  • Sujica, Aleksandar
  • Van Keilegom, Ingrid

Abstract

A common assumption when working with randomly right censored data, is the independence between the variable of interest Y (the survival time) and the censoring variable C. This assumption, which is not testable, is however unrealistic in certain situations. Let us assume that for a given covariate X, the dependence between the variables Y and C is described via a known copula. Additionally assume that Y is the response variable of a heteroscedastic regression model Y=m(X)+σ(X)ɛ, where the error term ε is independent of the explanatory variable X, and the functions m and σ are ‘smooth’. An estimator of the conditional distribution of Y given X under this model is then proposed, and the asymptotic normality of this estimator is shown. The small sample performance of the estimator is also studied, and the advantages/drawbacks of this estimator with respect to competing estimators are discussed.

Suggested Citation

  • Sujica, Aleksandar & Van Keilegom, Ingrid, 2018. "The copula-graphic estimator in censored nonparametric location-scale regression models," Econometrics and Statistics, Elsevier, vol. 7(C), pages 89-114.
    • Handle: RePEc:eee:ecosta:v:7:y:2018:i:c:p:89-114
    DOI: 10.1016/j.ecosta.2017.07.002
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    References listed on IDEAS

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    1. Juan Carlos Pardo‐Fernández & Ingrid Van Keilegom, 2006. "Comparison of Regression Curves with Censored Responses," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(3), pages 409-434, September.
    2. Arthur Lewbel & Oliver Linton, 2002. "Nonparametric Censored and Truncated Regression," Econometrica, Econometric Society, vol. 70(2), pages 765-779, March.
    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. Linton, Oliver & Mammen, Enno & Nielsen, Jens Perch & Van Keilegom, Ingrid, 2011. "Nonparametric regression with filtered data," LIDAM Reprints ISBA 2011008, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    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. Songnian Chen & Gordon B. Dahl & Shakeeb Khan, 2005. "Nonparametric Identification and Estimation of a Censored Location-Scale Regression Model," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 212-221, March.
    7. Sujica, Aleksandar & Van Keilegom, Ingrid, 2015. "Estimation of location and scale functionals in nonparametric regression under copula dependent censoring," LIDAM Reprints ISBA 2015016, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. 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.
    9. Rivest, Louis-Paul & Wells, Martin T., 2001. "A Martingale Approach to the Copula-Graphic Estimator for the Survival Function under Dependent Censoring," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 138-155, October.
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    Cited by:

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    2. Deresa, N.W. & Van Keilegom, I. & Antonio, K., 2022. "Copula-based inference for bivariate survival data with left truncation and dependent censoring," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 1-21.
    3. Lo, Simon M.S. & Wilke, Ralf A. & Emura, Takeshi, 2024. "A semiparametric model for the cause-specific hazard under risk proportionality," Computational Statistics & Data Analysis, Elsevier, vol. 195(C).

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