科研之友
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摘要
In this paper, we shall investigate a bootstrap method based on a martingale representation of the relevant statistic for inference to a class of functionals of the survival distribution. The method is similar in spirit to Efron's (1981) bootstrap, and thus in the present paper will be referred to as "martingale-based bootstrap". The method was derived from Lin, Wei and Ying (1993), who applied the method in checking the Cox model with cumulative sums of martingale-based residuals. It is shown that this martingale-based bootstrap gives a correct first-order asymptotic approximation to the distribution function of the corresponding functional of the Kaplan-Meier estimator. As a consequence, confidence intervals constructed by the martingale-based bootstrap have asymptotically correct coverage probability. Our simulation study indicates that the martingale-based bootstrap method for small and moderate sample sizes can be uniformly better than the usual bootstrap method in estimating the sampling distribution for a mean function and a point probability in survival analysis.
- 出版日期2000
- 单位北京大学
