We propose a new constrained EM algorithm that is applicable to general constrained estimation problems. The proposed method is based on a novel framework, the `dual-homotopy framework,' which combines deterministic annealing EM with a barrier-based optimization, enabling stable estimation under parameter constraints. Building on this framework, we further introduce an adaptive constrained EM algorithm that preserves likelihood monotonicity, regardless of the underlying distributional form or the specific structure of the constraints. Through simulation studies and a real-data analysis, both under parameter constraints, we demonstrate that the proposed algorithm yields more stable and accurate estimates than existing methods, including the standard EM algorithm.

翻译：我们提出一种新的约束EM算法，适用于一般的约束估计问题。该方法基于一个新颖的框架——"双同伦框架"，该框架将确定性退火EM与基于障碍函数的优化相结合，使得在参数约束下能够实现稳定估计。在此基础上，我们进一步引入一种自适应约束EM算法，该算法无论底层分布形式或约束的具体结构如何，都能保持似然函数的单调性。通过模拟研究和实际数据分析（均在参数约束条件下），我们证明所提出的算法相比现有方法（包括标准EM算法）能产生更稳定、更准确的估计。