Journal of multivariate analysis, 2008-05, Vol.99 (5), p.787-814
2008
Details
- Autor(en) / Beteiligte
- Titel
- Adaptive estimation of the transition density of a particular hidden Markov chain
- Ist Teil von
- Journal of multivariate analysis, 2008-05, Vol.99 (5), p.787-814
- Ort / Verlag
- San Diego, CA: Elsevier Inc
- Erscheinungsjahr
- 2008
- Link zum Volltext
- Quelle
- Alma/SFX Local Collection
- Beschreibungen/Notizen
- We study the following model of hidden Markov chain: Y i = X i + ɛ i , i = 1 , … , n + 1 with ( X i ) a real-valued positive recurrent and stationary Markov chain, and ( ɛ i ) 1 ⩽ i ⩽ n + 1 a noise independent of the sequence ( X i ) having a known distribution. We present an adaptive estimator of the transition density based on the quotient of a deconvolution estimator of the density of X i and an estimator of the density of ( X i , X i + 1 ) . These estimators are obtained by contrast minimization and model selection. We evaluate the L 2 risk and its rate of convergence for ordinary smooth and supersmooth noise with regard to ordinary smooth and supersmooth chains. Some examples are also detailed.
- Sprache
- Englisch
- Identifikatoren
- ISSN: 0047-259XeISSN: 1095-7243DOI: 10.1016/j.jmva.2007.04.006Titel-ID: cdi_hal_primary_oai_HAL_hal_00115612v1
- Format
- –
- Schlagworte
- Deconvolution, Estimating techniques, Exact sciences and technology, Hidden Markov chain, Hidden Markov chain Transition density Nonparametric estimation Deconvolution Model selection Rate of convergence, Markov analysis, Markov processes, Mathematical models, Mathematics, Model selection, Multivariate analysis, Nonparametric estimation, Nonparametric inference, Parametric inference, Probability and statistics, Probability theory and stochastic processes, Rate of convergence, Sciences and techniques of general use, Statistics, Statistics Theory, Studies, Transition density, Transitions