Sharp minimax distribution estimation for current status censoring with or without missing
有无缺失时当前状态删失下的精确极小极大分布估计AI 解读 ↓
← 返回论文列表与筛选
阅读说明
本页整理公开书目信息，不生成学术质量评分。AI 解读根据题名及所注明的摘要或原文片段生成，未完成全文核验，可能有误；具体假设、证明与结论请核对原文。摘要保留来源文本，未经模型改写。
DOI 首次登记不等于接收或发表日期。部分更正、评论等条目没有独立摘要；缺少可靠材料时保留待补状态。
引用量采用 OpenAlex 单条关联记录，不合计多个记录；关联记录可能包含正式发表版本，不等于此版本单独引用。缺失不视为零，引用指标不代表论文质量。
关注作者按书目中的完整姓名匹配，同名和姓名变体需人工辨别。相关论文先按共享细分方向和具体方法排列，再参考通用方法与发表日期。
分类依据与纠错
AI 根据所提供的论文材料归类：摘要聚焦删失寿命数据的通用分布估计，未研究分布效应或其他所列计量方向。
反馈分类问题
正在核对关联版本…
代码、数据与补充材料
正在核对对应版本的资源…
关注这篇论文的作者
有无缺失时当前状态删失下的精确极小极大分布估计
- 研究问题
- 仅观察寿命事件的当前状态，且监测时间可能因左右缺失而不可见时，如何处理观测偏倚并有效估计寿命分布与密度？
- 方法与思路
- 作者区分完整与缺失监测数据，利用已知监测密度或额外横截面样本，并结合极小极大分析及频域、时域平滑构造估计。
- 材料陈述的贡献
- 摘要称建立了精确极小极大估计理论，处理非周期索伯列夫函数逼近，并讨论已知分布函数平滑度时较粗糙监测密度的影响。
- 阅读关注点
- 应核对各观测机制下监测密度的可识别性、额外样本要求、效率常数，以及依赖寿命与监测时间扩展所需的条件。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要；偏倚函数条件、精确效率界及实例结果未给出，不能推断刊本变化。
原文摘要
Nonparametric estimation of the cumulative distribution function and the probability density of a lifetime X modified by a current status censoring (CSC), including cases of right and left missing data, is a classical ill-posed problem with biased data. The biased nature of CSC data may preclude us from consistent estimation unless the biasing function is known or may be estimated, and its ill-posed nature slows down rates of convergence. Under a traditionally studied CSC, we observe a sample from $(Z,\Delta )$ where a continuous monitoring time $Z$ is independent of $X$, $\Delta :=I(X\leq Z)$ is the status, and the bias of observations is created by the density of $Z$ which is estimable. In presence of right or left missing, we observe corresponding samples from $(\Delta Z,\Delta )$ or $((1-\Delta )Z,\Delta )$; the data are again biased but now the density of $Z$ cannot be estimated from the data. As a result, to solve the estimation problem, either the density of $Z$ must be known (like in a controlled study) or an extra cross-sectional sampling of $Z$, which is typically simpler than an underlying CSC study, be conducted. The main aim of the paper is to develop for this biased and ill-posed problem the theory of efficient (sharp-minimax) estimation which is inspired by known results for the case of directly observed $X$. Among interesting aspects of the developed theory: (i) While sharp-minimax analysis of missing CSC may follow the classical Pinsker’s methodology, analysis of CSC requires a more complicated estimation procedure based on a special smoothing in both frequency and time domains; (ii) Efficient estimation requires solving an old-standing problem of approximating aperiodic Sobolev functions; (iii) If smoothness of the cdf of $X$ is known, then its rate-minimax estimation is possible even if the density of $Z$ is rougher. Real and simulated examples, as well as extensions of the core models to dependent $X$ and Z and case-control CSC, are presented.