Parameter Estimation for Continuous Time Hidden Markov Processes

被引：0
作者：
Yu. A. Kutoyants
机构：
[1] Le Mans Université,
[2] Tomsk State University,undefined
来源：
Automation and Remote Control | 2020年 / 81卷
关键词：
parameter estimation; hidden processes; Kalman filtering; telegraph process;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
A survey of research works on the parameter estimation of hidden Markov processes is presented. Two observation models are considered: a partially observed two-dimensional Gaussian process and a telegraph process observed against the background of white Gaussian noise. The properties of estimators in the large sample and small noise asymptotics are described. Special attention is paid to the computational complexity and asymptotic efficiency of the estimators proposed.
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页码：445 / 468
页数：23
相关论文
共 17 条
  • [1] Bickel PJ(1998)Asymptotic Normality of the Maximum Likelihood Estimator for General Hidden Markov Models Ann. Statist. 26 1614-1635
  • [2] Ritov Y(1925)Theory of Statistical Estimation Proc. Cambridge Phylosoph. Soc. 22 700-725
  • [3] Rydén T(1956)On the Asymptotic Theory of Estimation and Testing Hypotheses Proc. 3rd Berkeley Sympos. I 355-368
  • [4] Fisher RA(2019)On Parameter Estimation of Hidden Ornstein—Uhlenbeck Process J. Multivariate Anal. 169 248-263
  • [5] Le Cam L(1967)On Filtration and Prediction of Components in Diffusion Markov Processes Theory Probab. Appl. 12 697-698
  • [6] Kutoyants YA(2000)Small Noise Asymptotics of the GLR Test for Offline Change Detection in Misspecified Diffusion Processes Stochast. Stochast. Report. 70 109-129
  • [7] Liptser RS(1991)Parameter Estimation in Linear Filtering J. Multivariate Anal. 39 284-304
  • [8] Campillo F(1996)A Minimum Distance Estimator for Partially Observed Linear Stochastic Systems Statist. Decisions 14 323-342
  • [9] Le Gland F(2009)Maximum Likelihood Estimation for Hidden Markov Models in Continuous Time Statist. Inference Stoch. Proc. 12 139-163
  • [10] Kutoyants YA(2018)On Parameter Estimation of Hidden Telegraph Process Bernoulli 24 2064-2090
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