Effects of Censoring on the Validity of Confidence Intervals
删失程度对置信区间有效性的影响AI 解读 ↓
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删失程度对置信区间有效性的影响
- 研究问题
- 当真实生存分布偏离指数分布时，增加删失能否改善基于指数模型估计量的分位数置信区间覆盖率，这种改善有何边界？
- 方法与思路
- 作者研究分位数估计量的一致渐近正态性与局部替代下的覆盖率，分析删失分布趋向零点质量的极限，并比较理论与模拟。
- 材料陈述的贡献
- 摘要称，偏离指数性的方式不依赖删失分布时，极限覆盖率恢复指数模型下水平；若二者相关，最不利方向的反例可使该结论失效。
- 阅读关注点
- 应核对一致渐近正态性的条件、局部替代与删失程度的联动方式，以及完全删失极限下反例和Weibull模拟的对应关系。
- 阅读边界
- 仅据OpenAlex索引摘要，稿件版本未注明。摘要没有列出完整正则条件；其极限结论不能推广为增加删失总会改善有限样本覆盖率。
原文摘要
This article examines how the level of censoring affects the validity of confidence intervals constructed from an exponential maximum likelihood estimator under departures from an assumed exponential survival distribution. The motivation for this work is a simulation study by Emerson (1981) suggesting that under Weibull departures from exponentiality, validity of confidence intervals for median survival time improves as censoring increases. To see if this result holds asymptotically in the case of complete censoring, first conditions are found under which the exponential maximum likelihood estimate of a percentile is asymptotically normal uniformly in F, where F is an arbitrary survival distribution function. Then, the asymptotic coverage probability of the exponential-based interval is found for a percentile of a local alternative to the exponential distribution. If the censoring distribution converges weakly to point mass at 0, and if the departure from exponentiality is independent of the censoring distribution, then the asymptotic coverage probability converges to the expected coverage probability under exponentiality. The least favorable direction of departure from exponentiality is found, and it is shown by counterexample that in the limiting case of complete censoring, if the departure from exponentiality depends on the censoring distribution as it does in the least favorable case, then the asymptotic coverage probability does not necessarily converge to the expected coverage probability under exponentiality. Finally, the results of this article are applied to uniformly censored Weibull alternatives, and the asymptotic-theory coverage probabilities are compared with simulated coverage probabilities.