Consistent order estimation for nonparametric hidden Markov models

DOI10.3150/17-BEJ993zbMath1442.62191arXiv1606.00622WikidataQ128754570 ScholiaQ128754570MaRDI QIDQ1715538

Luc Lehéricy

Publication date: 28 January 2019

Published in: Bernoulli (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1606.00622

zbMATH Keywords

model selectionhidden Markov modelspectral methodleast squares methodnonparametric density estimationorder estimation

Mathematics Subject Classification ID

Density estimation (62G07) Nonparametric estimation (62G05) Hypothesis testing in multivariate analysis (62H15) Non-Markovian processes: estimation (62M09) Order statistics; empirical distribution functions (62G30) Inference from stochastic processes and spectral analysis (62M15) Markov processes: estimation; hidden Markov models (62M05)

Related Items (4)

The order estimation for hidden Markov models ⋮ Learning the distribution of latent variables in paired comparison models with round-robin scheduling ⋮ Consistent order estimation for nonparametric hidden Markov models ⋮ State-by-state Minimax Adaptive Estimation for Nonparametric Hidden Markov Models

Uses Software

• CMA-ES
• CAPUSHE
• HMMmix

Cites Work

• Unnamed Item
• Unnamed Item
• Generalized reduced rank tests using the singular value decomposition
• Estimating multivariate latent-structure models
• A spectral algorithm for learning hidden Markov models
• About the posterior distribution in hidden Markov models with unknown number of states
• Selecting hidden Markov model state number with cross-validated likelihood
• Slope heuristics: overview and implementation
• Concentration inequalities and model selection. Ecole d'Eté de Probabilités de Saint-Flour XXXIII -- 2003.
• Hidden Markov models with mixtures as emission distributions
• A minimum description length approach to hidden Markov models with Poisson and Gaussian emissions. Application to order identification
• Identifiability of parameters in latent structure models with many observed variables
• Consistent order estimation for nonparametric hidden Markov models
• Asymptotic properties of the maximum likelihood estimator in autoregressive models with Markov regime
• Asymptotic normality of the maximum-likelihood estimator for general hidden Markov models
• Likelihood ratio inequalities with applications to various mixtures
• Exponential forgetting and geometric ergodicity in hidden Markov models
• Minimal penalties for Gaussian model selection
• Minimax adaptive estimation of nonparametric hidden Markov models
• Nonparametric inference in hidden Markov models using P‐splines
• The likelihood ratio test for the number of components in a mixture with Markov regime
• TESTS OF RANK
• Bayesian Non-Parametric Hidden Markov Models with Applications in Genomics
• Optimal error exponents in hidden markov models order estimation
• Consistent Estimation of the Filtering and Marginal Smoothing Distributions in Nonparametric Hidden Markov Models
• Nonparametric identification and maximum likelihood estimation for hidden Markov models

This page was built for publication: Consistent order estimation for nonparametric hidden Markov models