基于有效重要性抽样的隐马尔可夫模型估计
Estimation in hidden Markov models via efficient importance sampling
摘要：
给定一个离散时间有限状态隐马尔可夫模型的观测序列，我们想估计一个统计量的抽样分布。利用Bootstrap方法逼近多维参数的置信区域。在这种情况下，我们提出了一个有效的模拟重要性抽样公式。我们的方法包括构建一个局部渐近正态（LAN）家庭的概率分布周围的默认恢复规则，然后最小化的LAN家庭内的渐近方差。这个最小化问题的解决方案的特点是渐近最优的rescue计划，这是由倾斜公式。倾斜公式的实施是通过求解泊松方程来实现的。数值算例表明了所提出的重要性抽样方案的有效性。
英文摘要：
Given a sequence of observations from a discrete-time, finite-state hidden Markov model, we would like to estimate the sampling distribution of a statistic. The bootstrap method is employed to approximate the confidence regions of a multi-dimensional parameter. We propose an importance sampling formula for efficient simulation in this context. Our approach consists of constructing a locally asymptotically normal (LAN) family of probability distributions around the default resampling rule and then minimizing the asymptotic variance within the LAN family. The solution of this minimization problem characterizes the asymptotically optimal resampling scheme, which is given by a tilting formula. The implementation of the tilting formula is facilitated by solving a Poisson equation. A few numerical examples are given to demonstrate the efficiency of the proposed importance sampling scheme.
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