B1284
Title: Efficient semiparametric estimation and cut posterior contraction in semiparametric hidden markov models
Authors: Daniel Moss - University of Oxford (United Kingdom) [presenting]
Judith Rousseau - University of Oxford (United Kingdom)
Abstract: The problem of estimation in hidden markov models with finite state space and nonparametric emission distributions is considered. Efficient estimators for the transition matrix are exhibited, and a semiparametric bernstein-von mises result is deduced, extending existing work for mixture models. Following from this, a cut posterior approach is employed to jointly estimate the transition matrix and the emission distributions. A general theorem on contraction rates for such cut posterior approaches is derived, analogous to existing results for the bayesian posterior. This result is applied to obtain a contraction rate result for the emission distributions in our setting, by first proving an $L^1$ inversion inequality to go from marginals to emissions. Finally, simulation studies are provided to illustrate theoretical results.
