Consistency of the maximum likelihood estimator for general hidden Markov models

DOI10.1214/10-AOS834zbMath1209.62194arXiv0912.4480MaRDI QIDQ2429938

Randal Douc, Eric Moulines, Jimmy Olsson, Ramon van Handel

Publication date: 5 April 2011

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.4480

zbMATH Keywords

maximum likelihood estimationhidden Markov modelsstate space modelsstrong consistencyconcentration inequalities\(V\)-uniform ergodicity

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Markov processes: estimation; hidden Markov models (62M05) Statistical aspects of information-theoretic topics (62B10)

Related Items

Sparseness, consistency and model selection for Markov regime-switching Gaussian autoregressive models, Self-normalized Cramér-type moderate deviations under dependence, Asymptotic Analysis of a Matrix Latent Decomposition Model, Pathwise stochastic control with applications to robust filtering, Parametric estimation of hidden stochastic model by contrast minimization and deconvolution, On seasonal functional modeling under strong dependence, with applications to mechanically ventilated breathing activity, Statistical inference for dynamical systems: a review, Hoeffding's inequality for non-irreducible Markov models, Unnamed Item, Variational Bayes in State Space Models: Inferential and Predictive Accuracy, Maximum Likelihood Estimation in Markov Regime‐Switching Models With Covariate‐Dependent Transition Probabilities, Biased online parameter inference for state-space models, Evolutionary State-Space Model and Its Application to Time-Frequency Analysis of Local Field Potentials, Filtered likelihood for point processes, Asymptotic analysis of model selection criteria for general hidden Markov models, Consistency of Maximum Likelihood Parameter Estimation for Bivariate Markov Chains, Hidden Markov model for parameter estimation of a random walk in a Markov environment, On some recent advances on high dimensional Bayesian statistics, Posterior consistency for partially observed Markov models, Bayesian hypothesis testing in latent variable models, A semiparametric stochastic volatility model, Asymptotic properties of the maximum likelihood estimation in misspecified hidden Markov models, Modelling and coherent forecasting of zero-inflated count time series, Maximum likelihood estimation in hidden Markov models with inhomogeneous noise, Nonasymptotic control of the MLE for misspecified nonparametric hidden Markov models, Consistency of the maximum likelihood estimator in seasonal hidden Markov models, Parametric estimation of hidden Markov models by least squares type estimation and deconvolution, Consistency of maximum likelihood estimation for some dynamical systems, Unnamed Item, Posterior consistency for nonparametric hidden Markov models with finite state space, Conditional rotation between forecasting models, Bayes posterior convergence for loss functions via almost additive thermodynamic formalism

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Efficient likelihood estimation in state space models
• Markov chains and stochastic stability
• Hidden Markov models in finance
• The stability of conditional Markov processes and Markov chains in random environments
• A tail inequality for suprema of unbounded empirical processes with applications to Markov chains
• The strong ergodic theorem for densities: Generalized Shannon-McMillan- Breiman theorem
• Correlation functions of a function of a finite-state Markov process with application to channel kinetics
• Stochastic optimal control. The discrete time case
• Maximum-likelihood estimation for hidden Markov models
• The positive-divergence and blowing-up properties
• Regeneration and general Markov chains
• Bounds on regeneration times and convergence rates for Markov chains
• Hoeffding's inequality for uniformly ergodic Markov chains
• Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime
• Weak convergence and empirical processes. With applications to statistics
• Basic properties of the projective product with application to products of column-allowable nonnegative matrices
• Exponential forgetting and geometric ergodicity in hidden Markov models
• Inference in hidden Markov models.
• Leroux's method for general hidden Markov models
• A Liapounov bound for solutions of the Poisson equation
• Probability with Martingales
• Hidden Markov chains and the analysis of genome structure
• Hidden Markov Models for Speech Recognition
• Towards a Unified Approach for Proving Geometric Ergodicity and Mixing Properties of Nonlinear Autoregressive Processes
• Statistical Inference for Probabilistic Functions of Finite State Markov Chains
• Probabilistic Functions of Finite State Markov Chains
• Asymptotics of the maximum likelihood estimator for general hidden Markov models