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General Coverage Problems with Applications, and Bootstrap Method in SurvivalAnalysis and Reliability Theory

机译：应用中的一般覆盖问题，以及生存分析和可靠性理论中的Bootstrap方法

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By approximating the classical Product-Limit estimator of a distribution functionwith an average of lid random variables, we derive, for the first time in the literature, sufficient and necessary conditions for the rates of (both strong as well as weak laws) uniform convergence of the Product-Limit estimator over the whole line. These findings somehow fill a longstanding gap in the theory of Survival Analysis and provide a systematic tool handling other challenging problems when data are incomplete. In deriving our main results we also suggested a heurestic way of estimating the rates of convergence. To demonstrate its applications we prove a related conjecture of Gill and explain how a reliable confidence interval and band near the endpoint can be constructed.

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