一般非单调MAR缺失机制下非参数估计的渐近性质：一种非参数极大似然方法
Asymptotics of Nonparametric Estimation under General Non-monotone MAR Missingness: A Nonparametric Maximum Likelihood Approach
中文总结 AI 辅助
本文针对非单调MAR缺失情形，采用筛极大似然方法建立非参数估计的收敛速率，将其应用于密度估计时，所得估计量经EM算法近似后，在模拟中表现与使用完整数据的核密度估计器相当。
中文摘要 AI 辅助
缺失数据是实证研究中普遍存在的挑战，因此针对该挑战的方法数量不断增长，多重插补和逆概率加权是主流策略。尽管如此，理论保证仍然有限，尤其在具有挑战性的非单调随机缺失（MAR）情形下；现有保证往往局限于完全随机缺失、单调缺失或分块缺失等简化场景，或依赖于对缺失机制的限制性假设。本文利用筛极大似然理论，在MAR假设及自然正性条件下，建立了无需对缺失机制建模、且对缺失模式配置无限制的MAR下的一般收敛速率。将该结果应用于密度估计，表明对于任意给定的光滑度水平，完整数据密度可在Hölder类上达到极小极大速率，仅相差一个对数因子；缺失不影响速率，仅通过一个常数产生影响。该估计量在实践中可通过直接对不完整数据操作的简单期望最大化（EM）算法近似。在模拟中，其在广泛的缺失水平下表现与使用完整数据的核密度估计器相当。
英文摘要
Missing data constitute a pervasive challenge in empirical research. Consequently, there is an ever-growing number of methods designed to address this challenge, with multiple imputation and inverse probability weighting the dominant strategies. Despite this, theoretical guarantees remain limited, particularly in the challenging case of non-monotone missing at random (MAR). When guarantees exist, they are often confined to simplified settings such as missing completely at random, monotone or block-wise missingness, or rest on restrictive assumptions about the missingness mechanism. In this paper, we utilize the theory of sieve maximum likelihood to establish a general rate of convergence under MAR that requires no modeling of the missingness mechanism and no restriction on the configuration of missing patterns, beyond MAR itself and a natural positivity condition. Applying this result to density estimation, we show that the complete-data density can be estimated at the minimax rate over a Hölder class, up to a logarithmic factor, for any prescribed smoothness level. The missingness does not affect the rate and enters only through a constant. The estimator is approximated in practice by a simple expectation-maximization (EM) algorithm operating on the incomplete data directly. In simulations, it performs comparably to the kernel density estimator supplied with the complete data across a wide range of missingness levels.
