Title: On the Robustness of Mixture Models in the Presence of Hidden Markov Regimes with Covariate-Dependent Transition Probabilities Show Chinese title

Title: 混合模型在存在协变量依赖转换概率的隐藏马尔可夫状态下的稳健性

Abstract: This paper studies the robustness of quasi-maximum-likelihood (QML) estimation in hidden Markov models (HMMs) when the regime-switching structure is misspecified. Specifically, we examine the case where the true data-generating process features a hidden Markov regime sequence with covariate-dependent transition probabilities, but estimation proceeds under a simplified mixture model that assumes regimes are independent and identically distributed. We show that the parameters governing the conditional distribution of the observables can still be consistently estimated under this misspecification, provided certain regularity conditions hold. Our results highlight a practical benefit of using computationally simpler mixture models in settings where regime dependence is complex or difficult to model directly. Show Chinese abstract

Abstract: 本文研究了在隐马尔可夫模型（HMMs）中准最大似然（QML）估计的稳健性，当状态转换结构被错误指定时。具体来说，我们考察了这样一种情况：真实的数据生成过程具有带有协变量依赖转换概率的隐藏马尔可夫状态序列，但估计过程中采用了一个简化的混合模型，该模型假设各状态相互独立且分布相同。 我们证明，在这种错误设定下，只要满足某些正则条件，控制可观测变量条件分布的参数仍然可以一致估计。我们的结果显示，在状态依赖关系复杂或难以直接建模的情况下，使用计算上更简单的混合模型在实践中具有一定的优势。