In this paper, a new estimation framework, Maximum Ideal Likelihood Estimator (MILE), is proposed for general parametric models with latent variables and missing values. Instead of focusing on the marginal likelihood of the observed data as in many traditional approaches, the MILE directly considers the joint distribution of the complete dataset by treating the latent variables as parameters (the ideal likelihood). The MILE framework remains valid, even when traditional methods are not applicable, e.g., non-finite conditional expectation of the marginal likelihood function, via different optimization techniques and algorithms. The statistical properties of the MILE, such as the asymptotic equivalence to the Maximum Likelihood Estimation (MLE), are proved under some mild conditions, which facilitate statistical inference and prediction. Simulation studies illustrate that MILE outperforms traditional approaches with computational feasibility and scalability using existing and our proposed algorithms.

翻译：本文针对具有潜变量与缺失值的一般参数化模型，提出了一种新的估计框架——最大理想似然估计器（MILE）。与许多传统方法聚焦于观测数据的边际似然不同，MILE通过将潜变量视为参数（即理想似然），直接考虑完整数据集的联合分布。即使传统方法因边际似然函数的条件期望非有限等情形而失效时，MILE框架仍可通过不同的优化技术与算法保持有效性。在若干温和条件下，本文证明了MILE的统计性质（例如与最大似然估计的渐近等价性），从而为统计推断与预测提供了便利。仿真研究表明，利用现有及本文提出的算法，MILE在计算可行性与可扩展性方面均优于传统方法。