Kaplan-Meier estimate on the plane: Weak convergence, LIL, and the bootstrap
We consider estimation of the bivariate survival function F(s,t) under bivariate random right censoring. It is shown that the bivariate product integral estimator can be written as , where is a sum of mean zero iid processes and is a remainder term of order O((n-1logn)1/2 (n-1log logn)1/8) a.s. Using this representation we establish weak convergence of as well as the law of iterated logarithm. Similar results are obtained for the bootstrap version of .
Volume (Year): 29 (1989)
Issue (Month): 2 (May)
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