2013/12/19 by Ajay Jasra, Jasra, Ajay
Computer Science · Economics, Econometrics and Finance · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Financial Risk and Volatility Modeling #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.1312.5423
arxiv created 2013/12/19 · openalex publication_date 2013/12/19 · arxiv updated 2013/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the following article we consider the time-stability associated to the sequential Monte Carlo (SMC) estimate of the backward interpretation of Feynman-Kac Formulae. This is particularly of interest in the context of performing smoothing for hidden Markov models (HMMs). We prove a central limit theorem (CLT) under weaker assumptions than adopted in the literature. We then show that the associated asymptotic variance expression, for additive functionals grows at most linearly in time, under hypotheses that are weaker than those currently existing in the literature. The assumptions are verified for some state-space models.