双侧信息性随机删失下指数尺度的闭式估计
Closed-form estimation of the exponential scale under two-sided informative random censorship
- Navoi State University（纳沃伊国立大学）
- Gulistan State University（古利斯坦国立大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对双侧信息性随机删失下的指数寿命尺度估计，提出闭式伪最大似然估计量，无需迭代，具有精确Fisher一致性、强相合性与高渐近效率，并推广至比例风险类。
AI中文摘要：
我们在一个信息性模型下，根据从两侧随机删失的观测值来估计指数寿命的尺度参数，该模型中每个删失律是寿命生存函数的幂——这是Koziol–Green比例风险模型的双侧推广。将经验分布函数代入似然方程，得到一个闭式的伪最大似然估计量，该估计量只需对顺序统计量进行一次遍历即可计算，既不需要迭代也不需要数值优化。一个digamma恒等式表明该估计方程是精确的（而不仅仅是渐近的）Fisher一致的。在不对删失深度施加任何限制的情况下，建立了强相合性和渐近正态性；关键在于一个恒等式，它将底层的$L$-统计量重写，无需其无界得分函数，从而去除了经典极限定理会施加的条件。影响函数和渐近方差以多伽马函数显式给出，因此置信区间无需数值积分。相对于观测数据模型的信息界，在所考虑的设计中效率超过$98.6\%$，并在广泛扫描中保持在$96.2\%$以上。只需要模型的进入半部分：无论右删失律如何，估计量都保持精确的Fisher一致性和强相合性，并且指数性被证明是该自由度的精确代价。该构造逐字推广到具有已知基线的比例风险类。三个数据集说明了该过程，包括一个左删失是真实存在的队列。
英文摘要：
We estimate the scale of an exponential lifetime from observations censored randomly from both sides, under an informative model in which each censoring law is a power of the lifetime survival function -- a two-sided generalization of the Koziol--Green proportional hazards model. Substituting the empirical distribution function into the likelihood equation yields a closed-form pseudo-maximum-likelihood estimator of the scale that is computed in one pass over the order statistics and needs neither iteration nor numerical optimization. A digamma identity shows the estimating equation to be \emph{exactly}, not merely asymptotically, Fisher-consistent. Strong consistency and asymptotic normality are established with \emph{no restriction on the censoring depth}; the key is an identity that rewrites the underlying $L$-statistic without its unbounded score function and so removes the condition that classical limit theorems would impose. The influence function and the asymptotic variance are explicit in polygamma functions, so confidence intervals require no numerical integration. Against the information bound of the observed-data model the efficiency exceeds $98.6\%$ in the designs considered and stays above $96.2\%$ over a wide sweep. Only the entry half of the model is needed: the estimator remains exactly Fisher-consistent and strongly consistent whatever the right-censoring law, and exponentiality is shown to be the precise price of that freedom. The construction extends verbatim to a proportional hazards class with known baseline. Three data sets illustrate the procedure, including a cohort in which left censoring is genuine.
