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Strong consistency under proportional censorship when covariables are present

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  • Uña-Álvarez, Jacobo de
  • González-Manteiga, Wenceslao

Abstract

Let (X,Y) be the variable of interest, where Y is the possibly right-censored lifetime and X is a p-dimensional covariate. We introduce a generalized ACL (Abdushukurov, Cheng, Lin) estimator F~XY of FXY(x,y)=P(X[less-than-or-equals, slant]x,Y[less-than-or-equals, slant]y) and we prove [integral operator][phi] dF~XY-->[integral operator][phi] dFXY a.s. for any integrable function [phi] under an extended Koziol-Green model of proportional censorship.

Suggested Citation

  • Uña-Álvarez, Jacobo de & González-Manteiga, Wenceslao, 1999. "Strong consistency under proportional censorship when covariables are present," Statistics & Probability Letters, Elsevier, vol. 42(3), pages 283-292, April.
    • Handle: RePEc:eee:stapro:v:42:y:1999:i:3:p:283-292
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    References listed on IDEAS

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    1. Cheng, Philip E. & Lin, Gwo Dong, 1987. "Maximum likelihood estimation of a survival function under the koziol-green proportional hazards model," Statistics & Probability Letters, Elsevier, vol. 5(1), pages 75-80, January.
    2. Stute, W., 1993. "Consistent Estimation Under Random Censorship When Covariables Are Present," Journal of Multivariate Analysis, Elsevier, vol. 45(1), pages 89-103, April.
    3. Stute, Winfried, 1992. "Strong consistency under the Koziol--Green model," Statistics & Probability Letters, Elsevier, vol. 14(4), pages 313-320, July.
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