Adaptive estimation of the transition density of a Markov chain

Annales de l'institut Henri Poincare (B) Probability and Statistics

Volumn 43, Issue 5, 2007, Pages 571-597

  Lacour, Claire ^a  

^a UNIVERSITÉ PARIS DESCARTES   (France)

Author keywords

Adaptive estimation; Markov chain; Model selection; Penalized contrast; Transition density

Indexed keywords

EID: 34547236057     PISSN: 02460203     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.anihpb.2006.09.003     Document Type: Article

References (27)

1. Ango Nzé P. Critères d'ergodicité de quelques modèles à représentation markovienne. C. R. Acad. Sci. Paris Sér. I 315 12 (1992) 1301-1304
2. Athreya K.B., and Atuncar G.S. Kernel estimation for real-valued Markov chains. Sankhyā Ser. A 60 1 (1998) 1-17
3. Baraud Y., Comte F., and Viennet G. Adaptive estimation in autoregression or β-mixing regression via model selection. Ann. Statist. 29 3 (2001) 839-875
4. Barron A., Birgé L., and Massart P. Risk bounds for model selection via penalization. Probab. Theory Related Fields 113 3 (1999) 301-413
5. Basu A.K., and Sahoo D.K. On Berry-Esseen theorem for nonparametric density estimation in Markov sequences. Bull. Inform. Cybernet. 30 1 (1998) 25-39
6. Birgé L. Approximation dans les espaces métriques et théorie de l'estimation. Z. Wahrsch. Verw. Gebiete 65 2 (1983) 181-237
7. Birgé L., and Massart P. From model selection to adaptive estimation. Festschrift for Lucien Le Cam (1997), Springer, New York 55-87
8. Birgé L., and Massart P. Minimum contrast estimators on sieves: exponential bounds and rates of convergence. Bernoulli 4 3 (1998) 329-375
9. Bosq D. Sur l'estimation de la densité d'un processus stationnaire et mélangeant. C. R. Acad. Sci. Paris Sér. A-B 277 (1973) A535-A538
10. Chaleyat-Maurel M., and Genon-Catalot V. Computable infinite dimensional filters with applications to discretized diffusion processes. Stochastic Process. Appl. 116 10 (2006) 1447-1467
11. Clémençon S. Adaptive estimation of the transition density of a regular Markov chain. Math. Methods Statist. 9 4 (2000) 323-357
12. Comte F. Adaptive estimation of the spectrum of a stationary Gaussian sequence. Bernoulli 7 2 (2001) 267-298
13. Comte F., and Rozenholc Y. Adaptive estimation of mean and volatility functions in (auto-)regressive models. Stochastic Process. Appl. 97 1 (2002) 111-145
14. Comte F., and Rozenholc Y. A new algorithm for fixed design regression and denoising. Ann. Inst. Statist. Math. 56 3 (2004) 449-473
15. Doukhan P. Mixing. Properties and Examples. Lecture Notes in Statistics vol. 85 (1994), Springer-Verlag, New York
16. Doukhan P., and Ghindès M. Estimation de la transition de probabilité d'une chaîne de Markov Doëblin-récurrente. Étude du cas du processus autorégressif général d'ordre 1. Stochastic Process. Appl. 15 3 (1983) 271-293
17. Härdle W., Kerkyacharian G., Picard P., and Tsybakov A. Wavelets, Approximation, and Statistical Applications. Lecture Notes in Statistics vol. 129 (1998), Springer-Verlag, New York
18. Hernández-Lerma O., Esparza S.O., and Duran B.S. Recursive nonparametric estimation of nonstationary Markov processes. Bol. Soc. Mat. Mexicana (2) 33 2 (1988) 57-69
19. Hochmuth R. Wavelet characterizations for anisotropic Besov spaces. Appl. Comput. Harmon. Anal. 12 2 (2002) 179-208
20. ○ 2005-8:. http://www.math-info.univ-paris5.fr/map5/publis/titres05.html
21. Meyn S.P., and Tweedie R.L. Markov Chains and Stochastic Stability (1993), Springer-Verlag, London
22. Mokkadem A. Sur un modèle autorégressif non linéaire : ergodicité et ergodicité géométrique. J. Time Ser. Anal. 8 2 (1987) 195-204
23. Nikol'skiǐ S.M. Approximation of Functions of Several Variables and Imbedding Theorems (1975), Springer-Verlag, New York translated from the Russian by John M. Danskin, Jr., Die Grundlehren der Mathematischen Wissenschaften, Band 205
24. Pardoux E., and Veretennikov A.Y. On the Poisson equation and diffusion approximation. I. Ann. Probab. 29 3 (2001) 1061-1085
25. Roussas G.G. Nonparametric estimation in Markov processes. Ann. Inst. Statist. Math. 21 (1969) 73-87
26. Talagrand M. New concentration inequalities in product spaces. Invent. Math. 126 3 (1996) 505-563
27. Viennet G. Inequalities for absolutely regular sequences: application to density estimation. Probab. Theory Related Fields 107 4 (1997) 467-492