This paper develops a unified estimation framework, the Maximum Ideal Likelihood Estimation (MILE), for general parametric models with latent variables. Unlike traditional approaches relying on the marginal likelihood of the observed data, MILE directly exploits the joint distribution of the complete data by treating the latent variables as parameters (the ideal likelihood). Borrowing strength from optimisation techniques and algorithms, MILE is a broadly applicable framework in case that traditional methods fail, such as when the marginal likelihood has non-finite expectations. MILE offers a flexible and robust alternative to established techniques, including the Expectation-Maximisation algorithm and Markov chain Monte Carlo. We facilitate statistical inference of MILE on consistency, asymptotic distribution, and equivalence to the Maximum Likelihood Estimation, under some mild conditions. Extensive simulations illustrative real-data applications illustrate the empirical advantages of MILE, outperforming existing methods on computational feasibility and scalability.

翻译：本文针对具有潜变量的一般参数模型，提出了一种统一的估计框架——最大理想似然估计（MILE）。与传统方法依赖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），直接利用完整数据的联合分布。借助优化技术与算法，MILE在传统方法失效的情况下（例如当边际似然具有非有限期望时）成为一个广泛适用的框架。它为包括期望最大化算法和马尔可夫链蒙特卡洛在内的现有技术提供了一种灵活且稳健的替代方案。在一些温和条件下，我们为MILE在一致性、渐近分布以及与最大似然估计的等价性方面提供了统计推断支持。大量的模拟实验和实际数据应用展示了MILE的经验优势，其在计算可行性和可扩展性方面优于现有方法。