Adaptive estimation of the transition density of a Markov chain
Lacour, Claire
Annales de l'I.H.P. Probabilités et statistiques, Tome 43 (2007), p. 571-597 / Harvested from Numdam
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@article{AIHPB_2007__43_5_571_0,
     author = {Lacour, Claire},
     title = {Adaptive estimation of the transition density of a Markov chain},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {43},
     year = {2007},
     pages = {571-597},
     doi = {10.1016/j.anihpb.2006.09.003},
     mrnumber = {2347097},
     zbl = {1125.62087},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2007__43_5_571_0}
}

Lacour, Claire. Adaptive estimation of the transition density of a Markov chain. Annales de l'I.H.P. Probabilités et statistiques, Tome 43 (2007) pp. 571-597. doi : 10.1016/j.anihpb.2006.09.003. http://gdmltest.u-ga.fr/item/AIHPB_2007__43_5_571_0/

[1] P. Ango Nzé, Critères d'ergodicité de quelques modèles à représentation markovienne, C. R. Acad. Sci. Paris Sér. I 315 (12) (1992) 1301-1304. | MR 1194540 | Zbl 0761.60062

[2] K.B. Athreya, G.S. Atuncar, Kernel estimation for real-valued Markov chains, Sankhyā Ser. A 60 (1) (1998) 1-17. | MR 1714774 | Zbl 0977.62093

[3] Y. Baraud, F. Comte, G. Viennet, Adaptive estimation in autoregression or β-mixing regression via model selection, Ann. Statist. 29 (3) (2001) 839-875. | MR 1865343 | Zbl 1012.62034

[4] A. Barron, L. Birgé, P. Massart, Risk bounds for model selection via penalization, Probab. Theory Related Fields 113 (3) (1999) 301-413. | MR 1679028 | Zbl 0946.62036

[5] A.K. Basu, D.K. Sahoo, On Berry-Esseen theorem for nonparametric density estimation in Markov sequences, Bull. Inform. Cybernet. 30 (1) (1998) 25-39. | MR 1629735 | Zbl 0921.62039

[6] L. Birgé, Approximation dans les espaces métriques et théorie de l'estimation, Z. Wahrsch. Verw. Gebiete 65 (2) (1983) 181-237. | MR 722129 | Zbl 0506.62026

[7] L. Birgé, P. Massart, From model selection to adaptive estimation, in: Festschrift for Lucien Le Cam, Springer, New York, 1997, pp. 55-87. | MR 1462939 | Zbl 0920.62042

[8] L. Birgé, P. Massart, Minimum contrast estimators on sieves: exponential bounds and rates of convergence, Bernoulli 4 (3) (1998) 329-375. | MR 1653272 | Zbl 0954.62033

[9] D. Bosq, Sur l'estimation de la densité d'un processus stationnaire et mélangeant, C. R. Acad. Sci. Paris Sér. A-B 277 (1973) A535-A538. | MR 326958 | Zbl 0288.62018

[10] M. Chaleyat-Maurel, V. Genon-Catalot, Computable infinite dimensional filters with applications to discretized diffusion processes, Stochastic Process. Appl. 116 (10) (2006) 1447-1467. | MR 2260743 | Zbl 1122.93079

[11] S. Clémençon, Adaptive estimation of the transition density of a regular Markov chain, Math. Methods Statist. 9 (4) (2000) 323-357. | MR 1827473 | Zbl 1008.62076

[12] F. Comte, Adaptive estimation of the spectrum of a stationary Gaussian sequence, Bernoulli 7 (2) (2001) 267-298. | MR 1828506 | Zbl 0981.62075

[13] F. Comte, Y. Rozenholc, Adaptive estimation of mean and volatility functions in (auto-)regressive models, Stochastic Process. Appl. 97 (1) (2002) 111-145. | MR 1870963 | Zbl 1064.62046

[14] F. Comte, Y. Rozenholc, A new algorithm for fixed design regression and denoising, Ann. Inst. Statist. Math. 56 (3) (2004) 449-473. | MR 2095013 | Zbl 1057.62030

[15] P. Doukhan, Mixing. Properties and Examples, Lecture Notes in Statistics, vol. 85, Springer-Verlag, New York, 1994. | MR 1312160 | Zbl 0801.60027

[16] P. Doukhan, M. Ghindès, 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. | MR 711186 | Zbl 0515.62037

[17] W. Härdle, G. Kerkyacharian, P. Picard, A. Tsybakov, Wavelets, Approximation, and Statistical Applications, Lecture Notes in Statistics, vol. 129, Springer-Verlag, New York, 1998. | MR 1618204 | Zbl 0899.62002

[18] O. Hernández-Lerma, S.O. Esparza, B.S. Duran, Recursive nonparametric estimation of nonstationary Markov processes, Bol. Soc. Mat. Mexicana (2) 33 (2) (1988) 57-69. | MR 1110000 | Zbl 0732.62086

[19] R. Hochmuth, Wavelet characterizations for anisotropic Besov spaces, Appl. Comput. Harmon. Anal. 12 (2) (2002) 179-208. | MR 1884234 | Zbl 1003.42024

[20] C. Lacour, Nonparametric estimation of the stationary density and the transition density of a Markov chainhttp://www.math-info.univ-paris5.fr/map5/publis/titres05.html. | Zbl 1129.62028

[21] S.P. Meyn, R.L. Tweedie, Markov Chains and Stochastic Stability, Springer-Verlag, London, 1993. | MR 1287609 | Zbl 0925.60001

[22] A. Mokkadem, Sur un modèle autorégressif non linéaire : ergodicité et ergodicité géométrique, J. Time Ser. Anal. 8 (2) (1987) 195-204. | MR 886138 | Zbl 0621.60076

[23] S.M. Nikol'Skiĭ, Approximation of Functions of Several Variables and Imbedding Theorems, Springer-Verlag, New York, 1975, translated from the Russian by John M. Danskin, Jr., Die Grundlehren der Mathematischen Wissenschaften, Band 205. | MR 374877 | Zbl 0307.46024

[24] E. Pardoux, A.Y. Veretennikov, On the Poisson equation and diffusion approximation. I, Ann. Probab. 29 (3) (2001) 1061-1085. | MR 1872736 | Zbl 1029.60053

[25] G.G. Roussas, Nonparametric estimation in Markov processes, Ann. Inst. Statist. Math. 21 (1969) 73-87. | MR 247722 | Zbl 0181.45804

[26] M. Talagrand, New concentration inequalities in product spaces, Invent. Math. 126 (3) (1996) 505-563. | MR 1419006 | Zbl 0893.60001

[27] G. Viennet, Inequalities for absolutely regular sequences: application to density estimation, Probab. Theory Related Fields 107 (4) (1997) 467-492. | MR 1440142 | Zbl 0933.62029