2013/12/01 by Hock Peng Chan, Tze Leung Lai
Computer Science · Mathematics · #Applied mathematics #Artificial intelligence #Asymptotic analysis #Asymptotic distribution #Bayesian Methods and Mixture Models #Delta method #Estimator #Hidden Markov model #Kalman filter #Markov Chains and Monte Carlo Methods #Markov chain #Martingale (probability theory) #Martingale difference sequence #Mathematics #Particle filter #Statistics #Target Tracking and Data Fusion in Sensor Networks #math.ST #stat.TH
paper · pdf · doi:10.1214/13-aos1172
published as Annals of Statistics 2013, Vol. 41, No. 6, 2877-2904 · Published in at http://dx.doi.org/10.1214/13-AOS1172 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2013/12/01 · arxiv created 2013/12/18 · arxiv updated 2013/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
By making use of martingale representations, we derive the asymptotic normality of particle filters in hidden Markov models and a relatively simple formula for their asymptotic variances. Although repeated resamplings result in complicated dependence among the sample paths, the asymptotic variance formula and martingale representations lead to consistent estimates of the standard errors of the particle filter estimates of the hidden states.