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摘要翻译：
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域。在此背景下，我们提出了一个有效模拟的重要抽样公式。我们的方法包括围绕缺省重采样规则构造局部渐近正态(LAN)概率分布族，然后使LAN族内的渐近方差最小化。这个极小化问题的解刻画了渐近最优重采样方案，它由一个倾斜公式给出。通过求解泊松方程，简化了倾斜公式的实现。给出了几个数值例子，证明了所提出的重要性抽样方案的有效性。
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英文标题：
《Estimation in hidden Markov models via efficient importance sampling》
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作者：
Cheng-Der Fuh, Inchi Hu
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最新提交年份：
2007
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分类信息：
一级分类：Statistics 统计学
二级分类：Computation 计算
分类描述：Algorithms, Simulation, Visualization
算法、模拟、可视化
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一级分类：Mathematics 数学
二级分类：Statistics Theory 统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics 统计学
二级分类：Statistics Theory 统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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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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PDF链接：
https://arxiv.org/pdf/708.4152
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