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Nonparametric Regression with Censored Covariates

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  • Dabrowska, D. M.

Abstract

The paper discusses weak convergence results for an estimate of the conditional survival function F(t z) = Pr(T> t Z = z) where T is a multivariate response variable and Z is a vector of covariates. It is assumed that both T and Z are subject to right censoring. The estimate is obtained by kernel smoothing the empirical analogue of a product integral representation of multivariate survival functions. Under regularity conditions we show that a standardized version of the regression estimate converges weakly to a mean zero Gaussian process and give the form of the asymptotic covariance in the case of univariate response variables. As a by product we also discuss asymptotic normality results for density estimates based on the smoothed product integral estimate.

Suggested Citation

  • Dabrowska, D. M., 1995. "Nonparametric Regression with Censored Covariates," Journal of Multivariate Analysis, Elsevier, vol. 54(2), pages 253-283, August.
    • Handle: RePEc:eee:jmvana:v:54:y:1995:i:2:p:253-283
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    Cited by:

    1. Arthur Lewbel & Oliver Linton, 2002. "Nonparametric Censored and Truncated Regression," Econometrica, Econometric Society, vol. 70(2), pages 765-779, March.
    2. repec:iab:iabfme:200709(en is not listed on IDEAS
    3. Jing Qian & Sy Han Chiou & Jacqueline E. Maye & Folefac Atem & Keith A. Johnson & Rebecca A. Betensky, 2018. "Threshold regression to accommodate a censored covariate," Biometrics, The International Biometric Society, vol. 74(4), pages 1261-1270, December.
    4. Wilke, Ralf A. & Wichert, Laura, 2005. "Application of a simple nonparametric conditional quantile function estimator in unemployment duration analysis," ZEW Discussion Papers 05-67 [rev.], ZEW - Leibniz Centre for European Economic Research.
    5. Debbarh, Mohammed & Viallon, Vivian, 2008. "Testing additivity in nonparametric regression under random censorship," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2584-2591, November.
    6. Bobrowski, Sebastian & Chen, Hong & Döring, Maik & Jensen, Uwe & Schinköthe, Wolfgang, 2015. "Estimation of the lifetime distribution of mechatronic systems in the presence of a covariate: A comparison among parametric, semiparametric and nonparametric models," Reliability Engineering and System Safety, Elsevier, vol. 139(C), pages 105-112.
    7. Wichert, Laura & Wilke, Ralf A., 2007. "Simple nonparametric estimators for unemployment duration analysis," FDZ Methodenreport 200709_en, Institut für Arbeitsmarkt- und Berufsforschung (IAB), Nürnberg [Institute for Employment Research, Nuremberg, Germany].

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