Open Access
May 2007 Estimation in hidden Markov models via efficient importance sampling
Cheng-Der Fuh, Inchi Hu
Bernoulli 13(2): 492-513 (May 2007). DOI: 10.3150/07--BEJ5163


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.


Download Citation

Cheng-Der Fuh. Inchi Hu. "Estimation in hidden Markov models via efficient importance sampling." Bernoulli 13 (2) 492 - 513, May 2007.


Published: May 2007
First available in Project Euclid: 18 May 2007

zbMATH: 1127.62068
MathSciNet: MR2331261
Digital Object Identifier: 10.3150/07--BEJ5163

Keywords: bootstrap , Locally asymptotical normal , Markov random walk , Poisson equation , twisting formula

Rights: Copyright © 2007 Bernoulli Society for Mathematical Statistics and Probability

Vol.13 • No. 2 • May 2007
Back to Top