no. 2
L p adaptive density estimation in a β mixing framework
Annales de l'I.H.P. Probabilités et statistiques, Tome 34 (1998) no. 2, pp. 179-208. 
@article{AIHPB_1998__34_2_179_0,
     author = {Tribouley, Karine and Viennet, Gabrielle},
     title = {$L_p$ adaptive density estimation in a $\beta $ mixing framework},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {179--208},
     publisher = {Gauthier-Villars},
     volume = {34},
     number = {2},
     year = {1998},
     zbl = {0941.62041},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_1998__34_2_179_0/}
}
TY  - JOUR
AU  - Tribouley, Karine
AU  - Viennet, Gabrielle
TI  - $L_p$ adaptive density estimation in a $\beta $ mixing framework
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 1998
SP  - 179
EP  - 208
VL  - 34
IS  - 2
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPB_1998__34_2_179_0/
LA  - en
ID  - AIHPB_1998__34_2_179_0
ER  - 
%0 Journal Article
%A Tribouley, Karine
%A Viennet, Gabrielle
%T $L_p$ adaptive density estimation in a $\beta $ mixing framework
%J Annales de l'I.H.P. Probabilités et statistiques
%D 1998
%P 179-208
%V 34
%N 2
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPB_1998__34_2_179_0/
%G en
%F AIHPB_1998__34_2_179_0
Tribouley, Karine; Viennet, Gabrielle. $L_p$ adaptive density estimation in a $\beta $ mixing framework. Annales de l'I.H.P. Probabilités et statistiques, Tome 34 (1998) no. 2, pp. 179-208. http://www.numdam.org/item/AIHPB_1998__34_2_179_0/

[1] P. Ango Nze and P. Doukhan, Functional estimation for time series : a general approach, Prépublication, Université Paris Sud, France, Vol. 93-43, 1993.

[2] H.C.P. Berbee, Random walks with stationary increments and renewal theory, Cent. Math. Tracts, Amsterdam, 1979. | MR | Zbl

[3] L. Birgé and P. Massart, Rates of convergence for minimum contrast estimators, Theor. Probab. Appl., Vol. 97, 1993, pp. 113-150. | MR | Zbl

[4] L. Birgé and P. Massart, From model selection to adaptative estimation, Prépublication, Université Paris Sud, France, Vol. 95-41, 1995.

[5] R. Dalhaus, M. Neumman and R. Von Sachs, Nonlinear wavelet estimation of time varying autoregressive processes, WIAS, Vol. 159, 1995.

[6] I. Daubechies, Orthogonal bases of compactly supported wavelets, Comm. in Pure and Applied Math., Vol. 41, 1988, pp 906-996. | MR | Zbl

[7] D.L. Donoho, I.M. Johnstone, G. Kerkyacharian and D. Picard, Density estimation by wavelet thresholding, Annals of Stat., Vol. 24, 1996, pp. 508-539. | MR | Zbl

[8] P. Doukhan, Mixing : properties and examples, Lecture Notes in Statistics, Springer Verlag, Vol. 72, 1994. | MR | Zbl

[9] P. Doukhan, P. Massart and E. Rio, The functional central limit theorem for strongly mixing processes, Ann. Inst. Henri Poincaré, Probab. Stat., Vol. 30, 1994, pp. 63-82. | EuDML | Numdam | MR | Zbl

[10] S.Y. Efroimovitch, Nonparametric estimation of a density of unknown smoothness, Theory Prob. Appl, Vol. 30, 1985, pp. 557-661. | Zbl

[11] S.Y. Efroimovich and M.S. Pinsker, Learning algorithm for nonparametric filtering, Automat. Remote Control, Vol. 11, 1984, pp. 1434-1440. | Zbl

[12] M. Hoffmann, On adaptive estimation in nonlinear AR(1) models, 1997 (Submitted).

[13] G. Kerkyacharian and D. Picard, Density estimation in Besov Spaces, Statistics and Probability Letters, Vol. 13, 1992a pp. 15-24. | MR | Zbl

[14] G. Kerkyacharian, D. Picard and K. Tribouley, Lp adaptative density estimation, Bernoulli, Vol. 2, 1996, pp. 229-247. | MR | Zbl

[15] A.N. Kolmogorov and Y.A. Rozanov, On the strong mixing conditions for stationary gaussian sequences, Theor. Probab. Appl., Vol. 5, 1960, pp. 204-207. | Zbl

[16] M. Ledoux and M. Talagrand, Probability in Banach spaces, A series of Modern Surveys in Mathematics, 1990, Springer, New York. | MR | Zbl

[17] Y. Meyer, Ondelettes, Paris, 1990, Hermann. | MR | Zbl

[18] A.S. Nemirovskii, Nonparametric estimation of smooth regression functions, J. Comput. Syst. Sci., Vol. 23, 1986, pp. 1-11. | MR | Zbl

[19] H.P. Rosenthal, On the subspace of Lp, p > 2, spanned by sequences of independent random variables, Israel J. Math., Vol. 8, 1970, pp. 273-303. | MR | Zbl

[20] B.W. Silverman, Density Estimation for Statistics and Data Analysis, Chapman and Hall, London, 1986. | MR | Zbl

[21] M. Talagrand, Sharper bounds for gaussian and empirical processes, Ann. Probab., Vol. 22, 1994, pp. 28-76. | MR | Zbl

[22] M. Talagrand, New concentration inequalities in product spaces, Technical Report, Universite Paris VI, Ohio State University, 1995. | MR

[23] G. Viennet, Inequalities for absolutely regular sequences: application to density estimation, Probab. Th. Rel. Fields, Vol. 107, 1997, pp 467-492. | MR | Zbl