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STRONG EMBEDDING OF PRODUCT-LIMIT ESTIMATOR OF BIVARIATE SURVIVAL DISTRIBUTION FUNCTION UNDER RANDOM CENSORSHIP
Wang Qihua
Acta mathematica scientia,Series B. 1995, 15 (S1):
123-132.
Let (Xi0,Yi0), 1 ≤ i ≤ n be i. i. d nonnegative random vectors with continuous survival distribution function be the product-limit estimator of S(s,t)=P(X0 > s,Y0 > t). Let Sn(s,t) be the product-limit estimator of S(s,t) suggested by Campbell and Földes (1980). In this paper it is shown that under some conditions a sequence of Gaussian processes Gn(s,t) can be constructed such that sup0T0S|n(1)/2[Sn(s,t)-S(s,t)]-Gn(s,t)|=O(n-(1)/2 log2n) a. s.,for S,T which together satisfy a certain condition.
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