Adaptive estimation of the transition density of a Markov chain

Claire Lacour

Annales de l'I.H.P. Probabilités et statistiques (2007)

  • Volume: 43, Issue: 5, page 571-597
  • ISSN: 0246-0203

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Lacour, Claire. "Adaptive estimation of the transition density of a Markov chain." Annales de l'I.H.P. Probabilités et statistiques 43.5 (2007): 571-597. <http://eudml.org/doc/77946>.

@article{Lacour2007,
author = {Lacour, Claire},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {adaptive estimation; transition density; Markov chain; model selection; penalized contrast},
language = {eng},
number = {5},
pages = {571-597},
publisher = {Elsevier},
title = {Adaptive estimation of the transition density of a Markov chain},
url = {http://eudml.org/doc/77946},
volume = {43},
year = {2007},
}

TY - JOUR
AU - Lacour, Claire
TI - Adaptive estimation of the transition density of a Markov chain
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2007
PB - Elsevier
VL - 43
IS - 5
SP - 571
EP - 597
LA - eng
KW - adaptive estimation; transition density; Markov chain; model selection; penalized contrast
UR - http://eudml.org/doc/77946
ER -

References

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  1. [1] P. Ango Nzé, Critères d'ergodicité de quelques modèles à représentation markovienne, C. R. Acad. Sci. Paris Sér. I315 (12) (1992) 1301-1304. Zbl0761.60062MR1194540
  2. [2] K.B. Athreya, G.S. Atuncar, Kernel estimation for real-valued Markov chains, Sankhyā Ser. A60 (1) (1998) 1-17. Zbl0977.62093MR1714774
  3. [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. Zbl1012.62034
  4. [4] A. Barron, L. Birgé, P. Massart, Risk bounds for model selection via penalization, Probab. Theory Related Fields113 (3) (1999) 301-413. Zbl0946.62036MR1679028
  5. [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. Zbl0921.62039
  6. [6] L. Birgé, Approximation dans les espaces métriques et théorie de l'estimation, Z. Wahrsch. Verw. Gebiete65 (2) (1983) 181-237. Zbl0506.62026MR722129
  7. [7] L. Birgé, P. Massart, From model selection to adaptive estimation, in: Festschrift for Lucien Le Cam, Springer, New York, 1997, pp. 55-87. Zbl0920.62042MR1462939
  8. [8] L. Birgé, P. Massart, Minimum contrast estimators on sieves: exponential bounds and rates of convergence, Bernoulli4 (3) (1998) 329-375. Zbl0954.62033MR1653272
  9. [9] D. Bosq, Sur l'estimation de la densité d'un processus stationnaire et mélangeant, C. R. Acad. Sci. Paris Sér. A-B277 (1973) A535-A538. Zbl0288.62018MR326958
  10. [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. Zbl1122.93079MR2260743
  11. [11] S. Clémençon, Adaptive estimation of the transition density of a regular Markov chain, Math. Methods Statist.9 (4) (2000) 323-357. Zbl1008.62076MR1827473
  12. [12] F. Comte, Adaptive estimation of the spectrum of a stationary Gaussian sequence, Bernoulli7 (2) (2001) 267-298. Zbl0981.62075MR1828506
  13. [13] F. Comte, Y. Rozenholc, Adaptive estimation of mean and volatility functions in (auto-)regressive models, Stochastic Process. Appl.97 (1) (2002) 111-145. Zbl1064.62046MR1870963
  14. [14] F. Comte, Y. Rozenholc, A new algorithm for fixed design regression and denoising, Ann. Inst. Statist. Math.56 (3) (2004) 449-473. Zbl1057.62030MR2095013
  15. [15] P. Doukhan, Mixing. Properties and Examples, Lecture Notes in Statistics, vol. 85, Springer-Verlag, New York, 1994. Zbl0801.60027MR1312160
  16. [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. Zbl0515.62037MR711186
  17. [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. Zbl0899.62002MR1618204
  18. [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. Zbl0732.62086MR1110000
  19. [19] R. Hochmuth, Wavelet characterizations for anisotropic Besov spaces, Appl. Comput. Harmon. Anal.12 (2) (2002) 179-208. Zbl1003.42024MR1884234
  20. [20] C. Lacour, Nonparametric estimation of the stationary density and the transition density of a Markov chain, Preprint MAP5 n 2005-8:,http://www.math-info.univ-paris5.fr/map5/publis/titres05.html. Zbl1129.62028
  21. [21] S.P. Meyn, R.L. Tweedie, Markov Chains and Stochastic Stability, Springer-Verlag, London, 1993. Zbl0925.60001MR1287609
  22. [22] A. Mokkadem, Sur un modèle autorégressif non linéaire : ergodicité et ergodicité géométrique, J. Time Ser. Anal.8 (2) (1987) 195-204. Zbl0621.60076MR886138
  23. [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. Zbl0307.46024MR374877
  24. [24] E. Pardoux, A.Y. Veretennikov, On the Poisson equation and diffusion approximation. I, Ann. Probab.29 (3) (2001) 1061-1085. Zbl1029.60053MR1872736
  25. [25] G.G. Roussas, Nonparametric estimation in Markov processes, Ann. Inst. Statist. Math.21 (1969) 73-87. Zbl0181.45804MR247722
  26. [26] M. Talagrand, New concentration inequalities in product spaces, Invent. Math.126 (3) (1996) 505-563. Zbl0893.60001MR1419006
  27. [27] G. Viennet, Inequalities for absolutely regular sequences: application to density estimation, Probab. Theory Related Fields107 (4) (1997) 467-492. Zbl0933.62029MR1440142

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