二元竞争风险场合二元PL估计的弱收敛性及其Bootstrap结果(英文)

Weak Convergence and Bootstrap of Bivariate Product Limit Estimators under the Bivariate Competing Risks Case

中文摘要:

      本文考虑了在二元竞争风险场合下二元PL估计的问题.文中给出了关于二元PL估计的独立同分布表达式,即将估计的差表为均值为零的独立同分布过程的和,且其余项的阶为O((u^-1logn)^3/4)a.s.,并证明该过程弱收敛到一个二元Gauss过程.关于Bootstrap情况也得到了类似的结果.

英文摘要:

      This paper considers estimation of the bivariate survival function under the bivariate competing risks case. We give an iid representation for the PL estimator which is iid mean zero process and the remainder term is of order O((n^-1 logn)^3/4) a.s., weak convergence of the process to a two-dimensional-time Gaussian process is shown. Similar results are obtained for the bootstrap version.