Name
Abstract | ||
|---|---|---|
We consider stationary hidden Markov models with finite state space and nonparametric modeling of the emission distributions. It has remained unknown until very recently that such models are identifiable. In this paper, we propose a new penalized least-squares estimator for the emission distributions which is statistically optimal and practically tractable. We prove a non asymptotic oracle inequality for our nonparametric estimator of the emission distributions. A consequence is that this new estimator is rate minimax adaptive up to a logarithmic term. Our methodology is based on projections of the emission distributions onto nested subspaces of increasing complexity. The popular spectral estimators are unable to achieve the optimal rate but may be used as initial points in our procedure. Simulations are given that show the improvement obtained when applying the least-squares minimization consecutively to the spectral estimation. |
Year | Venue | Keywords |
|---|---|---|
2016 | JOURNAL OF MACHINE LEARNING RESEARCH | nonparametric estimation,hidden Markov models,minimax adaptive estimation,oracle inequality,penalized least-squares |
Field | DocType | Volume |
Applied mathematics,Minimax,Minimax estimator,Artificial intelligence,Concentration inequality,Mathematical optimization,Spectral density estimation,Pattern recognition,Model selection,Nonparametric statistics,Hidden Markov model,Mathematics,Estimator | Journal | 17 |
ISSN | Citations | PageRank |
1532-4435 | 0 | 0.34 |
References | Authors | |
0 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yohann de Castro | 1 | 28 | 6.39 |
| Elisabeth Gassiat | 2 | 38 | 5.21 |
| claire lacour | 3 | 0 | 0.34 |