$L_p$ adaptive density estimation in a $\beta$ mixing framework

 Access to full text

 Full (PDF)

1. [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. [2] H.C.P. Berbee, Random walks with stationary increments and renewal theory, Cent. Math. Tracts, Amsterdam, 1979. Zbl0443.60083MR547109
3. [3] L. Birgé and P. Massart, Rates of convergence for minimum contrast estimators, Theor. Probab. Appl., Vol. 97, 1993, pp. 113-150. Zbl0805.62037MR1240719
4. [4] L. Birgé and P. Massart, From model selection to adaptative estimation, Prépublication, Université Paris Sud, France, Vol. 95-41, 1995. 
5. [5] R. Dalhaus, M. Neumman and R. von Sachs, Nonlinear wavelet estimation of time varying autoregressive processes, WIAS, Vol. 159, 1995. 
6. [6] I. Daubechies, Orthogonal bases of compactly supported wavelets, Comm. in Pure and Applied Math., Vol. 41, 1988, pp 906-996. Zbl0644.42026MR951745
7. [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. Zbl0860.62032MR1394974
8. [8] P. Doukhan, Mixing : properties and examples, Lecture Notes in Statistics, Springer Verlag, Vol. 72, 1994. Zbl0801.60027MR1312160
9. [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. Zbl0790.60037MR1262892
10. [10] S.Y. Efroimovitch, Nonparametric estimation of a density of unknown smoothness, Theory Prob. Appl, Vol. 30, 1985, pp. 557-661. Zbl0593.62034
11. [11] S.Y. Efroimovich and M.S. Pinsker, Learning algorithm for nonparametric filtering, Automat. Remote Control, Vol. 11, 1984, pp. 1434-1440. Zbl0637.93069
12. [12] M. Hoffmann, On adaptive estimation in nonlinear AR(1) models, 1997 (Submitted). 
13. [13] G. Kerkyacharian and D. Picard, Density estimation in Besov Spaces, Statistics and Probability Letters, Vol. 13, 1992a pp. 15-24. Zbl0749.62026MR1147634
14. [14] G. Kerkyacharian, D. Picard and K. Tribouley, Lp adaptative density estimation, Bernoulli, Vol. 2, 1996, pp. 229-247. Zbl0858.62031MR1416864
15. [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. Zbl0106.12005
16. [16] M. Ledoux and M. Talagrand, Probability in Banach spaces, A series of Modern Surveys in Mathematics, 1990, Springer, New York. Zbl0748.60004MR1102015
17. [17] Y. Meyer, Ondelettes, Paris, 1990, Hermann. Zbl0694.41037MR1085487
18. [18] A.S. Nemirovskii, Nonparametric estimation of smooth regression functions, J. Comput. Syst. Sci., Vol. 23, 1986, pp. 1-11. Zbl0604.62033MR844292
19. [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. Zbl0213.19303MR271721
20. [20] B.W. Silverman, Density Estimation for Statistics and Data Analysis, Chapman and Hall, London, 1986. Zbl0617.62042MR848134
21. [21] M. Talagrand, Sharper bounds for gaussian and empirical processes, Ann. Probab., Vol. 22, 1994, pp. 28-76. Zbl0798.60051MR1258865
22. [22] M. Talagrand, New concentration inequalities in product spaces, Technical Report, Universite Paris VI, Ohio State University, 1995. MR1419006
23. [23] G. Viennet, Inequalities for absolutely regular sequences: application to density estimation, Probab. Th. Rel. Fields, Vol. 107, 1997, pp 467-492. Zbl0933.62029MR1440142

1. Fabienne Comte, Florence Merlevède, Adaptive estimation of the stationary density of discrete and continuous time mixing processes
2. Fabienne Comte, Florence Merlevède, Adaptive estimation of the stationary density of discrete and continuous time mixing processes
3. Irène Gannaz, Olivier Wintenberger, Adaptive density estimation under weak dependence