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Nonparametric rank based estimation of bivariate densities given censored data conditional on marginal probabilities

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  • Alan D. Hutson

    (Department of Biostatistics and Bioinformatics)

Abstract

In this note we develop a new Kaplan-Meier product-limit type estimator for the bivariate survival function given right censored data in one or both dimensions. Our derivation is based on extending the constrained maximum likelihood density based approach that is utilized in the univariate setting as an alternative strategy to the approach originally developed by Kaplan and Meier (1958). The key feature of our bivariate survival function is that the marginal survival functions correspond exactly to the Kaplan-Meier product limit estimators. This provides a level of consistency between the joint bivariate estimator and the marginal quantities as compared to other approaches. The approach we outline in this note may be extended to higher dimensions and different censoring mechanisms using the same techniques.

Suggested Citation

  • Alan D. Hutson, 2016. "Nonparametric rank based estimation of bivariate densities given censored data conditional on marginal probabilities," Journal of Statistical Distributions and Applications, Springer, vol. 3(1), pages 1-14, December.
    • Handle: RePEc:spr:jstada:v:3:y:2016:i:1:d:10.1186_s40488-016-0047-y
    DOI: 10.1186/s40488-016-0047-y
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    References listed on IDEAS

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    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. Ross L. Prentice & F. Zoe Moodie & Jianrong Wu, 2004. "Hazard‐based nonparametric survivor function estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(2), pages 305-319, May.
    3. Michael G. Akritas & Ingrid Van Keilegom, 2003. "Estimation of bivariate and marginal distributions with censored data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 457-471, May.
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    Cited by:

    1. Sangita Kulathinal & Isha Dewan, 2023. "Weighted U-statistics for likelihood-ratio ordering of bivariate data," Statistical Papers, Springer, vol. 64(2), pages 705-735, April.

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