TY - JOUR
T1 - Inference in hidden Markov models I
T2 - Local asymptotic normality in the stationary case
AU - Bickel, Peter J.
AU - Ritov, Ya’acov
PY - 1996/1/1
Y1 - 1996/1/1
N2 - Following up on work by Baum and Petrie published 30 years ago, we study likelihood-based methods in hidden Markov models, where the hiding mechanism can lead to continuous observations and is itself governed by a parametric model. We show that procedures essentially equivalent to maximum likelihood estimates are asymptotically normal as expected and consistent estimates of their variance can be constructed, so that the usual inferential procedures are asymptotically valid.
AB - Following up on work by Baum and Petrie published 30 years ago, we study likelihood-based methods in hidden Markov models, where the hiding mechanism can lead to continuous observations and is itself governed by a parametric model. We show that procedures essentially equivalent to maximum likelihood estimates are asymptotically normal as expected and consistent estimates of their variance can be constructed, so that the usual inferential procedures are asymptotically valid.
KW - Geometric ergodicity
KW - Hidden Markov models
KW - Local asymptotic normality
KW - Maximum likelihood
UR - http://www.scopus.com/inward/record.url?scp=0000729652&partnerID=8YFLogxK
U2 - 10.3150/bj/1178291719
DO - 10.3150/bj/1178291719
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AN - SCOPUS:0000729652
SN - 1350-7265
VL - 2
SP - 199
EP - 228
JO - Bernoulli
JF - Bernoulli
IS - 3
ER -