AI 中文总结
本研究针对存在删失数据的Cox模型，推导了回归系数的效率界，证明了Cox的精确估计量渐近有效，并提出了计算复杂度更低的等价估计量。
AI 中文摘要
Cox模型及其回归系数在应用研究中被广泛使用，不过对应的统计理论主要是在无删失失效时间的连续情形下发展的。本研究在不假设失效分布为连续或离散的条件下，推导了Cox模型中回归系数的效率界；在总体失效质量点属于未知有限集的技术假设下，证明了Cox（1972）提出的“精确”估计量具有渐近有效性；还提出了一种求解有效得分的渐近等价估计量，其计算复杂度低于精确Cox得分。该研究采用了近期提出的鞅理论，对绝对连续和离散两种情形均给出了一般理论的实例。
英文摘要
The Cox model and the Cox regression coefficient are widely used in applied work, although the corresponding statistical theory is principally developed in the continuous case where there can be no tied failure times. In this work, we derive the efficiency bound of the Cox regression coefficient in the Cox model, without imposing continuity or discreteness assumptions on the failure distribution. Then, under a technical assumption that the population failure mass points belong to an unknown finite set, we show that the ``exact'' estimator in \citet{cox1972regression} is asymptotically efficient. Next, we propose an asymptotically equivalent estimator which solves the efficient score which has lower computational complexity than the exact Cox score. The development employs recently introduced martingale theory, and throughout examples of the general theory are given for both the absolutely continuous case and the discrete case.
