Adaptive sampling schemes for density estimation

Journal of Statistical Planning and Inference

Volumn 136, Issue 9, 2006, Pages 2898-2917

  Blanke, Delphine ^a  

^a SORBONNE UNIVERSITÉ   (France)

Author keywords

Adaptive estimation; Continuous time; Density estimation; Kernel estimator; Pointwise estimation; Sampling scheme

Indexed keywords

EID: 33747506887     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2004.12.005     Document Type: Article

References (38)

1. Barndorff-Nielsen O.E., and Pérez-Abreu V. Stationary and self-similar processes driven by Lévy processes. Stochastic Process. Appl. 84 2 (1999) 357-369
2. Birgé, L., Massart, P., 1997. From model selection to adaptive estimation. in: Pollard, D., Torgersen, E., Yang, G.L. (Eds.), Festschrift for Lucien Le Cam. Springer, New York, pp. 55-87.
3. Blanke, D., 2004. Sample paths adaptive density estimator, Math. Methods Statist., 13 (2), 123-152.
4. Blanke D., and Bosq D. Accurate rates of density estimators for continuous time processes. Statist. Probab. Lett. 33 2 (1997) 185-191
5. Blanke D., and Bosq D. A family of minimax rates for density estimators in continuous time. Stochastic Anal. Appl. 18 6 (2000) 871-900
6. Blanke D., and Pumo B. Optimal sampling for density estimation in continuous time. J. Time Ser. Anal. 24 1 (2003) 1-24
7. Bosq D. Sur le comportement exotique de l'estimateur à noyau de la densité marginale d'un processus à temps continu. C.R. Acad. Sci. Paris Sér. I Math. 320 3 (1995) 369-372
8. Bosq D. Parametric rates of nonparametric estimators and predictors for continuous time processes. Ann. Statist. 25 3 (1997) 982-1000
9. Bosq, D., 1998. Nonparametric statistics for stochastic processes. Estimation and Prediction, Lecture Notes in Statistics, vol. 110, second ed. Springer, New York.
10. Bosq D., and Cheze-Payaud N. Optimal asymptotic quadratic error of nonparametric regression function estimates for a continuous-time process from sampled-data. Statistics 32 3 (1999) 229-247
11. Bosq D., and Davydov Y. Local time and density estimation in continuous time. Math. Methods Statist. 8 (1999) 22-45
12. Butucea C. Exact adaptive pointwise estimation on Sobolev classes of densities. ESAIM Probab. Statist. 5 (2001) 1-31
13. Castellana J.V., and Leadbetter M.R. On smoothed probability density estimation for stationary processes. Stochastic Process. Appl. 21 (1986) 179-193
14. Comte F., and Merlevède F. Adaptive estimation of the stationary density of discrete and continuous time mixing processes. ESAIM Probab. Statist. 6 (2002) 211-238
15. Comte, F., Merlevède, F., 2002b. Density estimation for a class of continuous time or discretely observed processes. Stochastic Process. Appl., to appear.
16. Donoho D.L., Johnstone I., Kerkyacharian G., and Picard D. Density estimation by wavelet thresholding. Ann. Statist. 24 2 (1996) 508-539
17. Efromovich S. Adaptive orthogonal series density estimation for small samples. Comput. Statist. Data Anal. 22 6 (1996) 599-617
18. Hall P., Lahiri S.N., and Truong Y.K. On bandwidth choice for density estimation with dependent data. Ann. Statist. 23 (1995) 2241-2263
19. Hart J.D., and Vieu P. Data-driven bandwidth choice for density estimation based on dependent data. Ann. Statist. 18 (1990) 873-890
20. Kim T.Y. Asymptotically optimal bandwidth selection rules for the kernel density estimator with dependent observations. J. Statist. Plann. Inference 59 2 (1997) 321-336
21. Kutoyants Y.A. Some problems of nonparametric estimation by observations of ergodic diffusion processes. Statist. Probab. Lett. 32 3 (1997) 311-320
22. Kutoyants Y.A. Efficiency density estimation for ergodic diffusion process. Statist. Inference Stochastic Process. 1 2 (1999) 131-155
23. Kutoyants Y.A. Statistical Inference for Ergodic Diffusion Processes, Series in Statistics (2003), Springer, Berlin
24. Leblanc, F., 1995. Discretized wavelet density estimators for continuous time stochastic processes. Wavelets and Statistics (Villard de Lans, 1994). Lecture Notes in Statistics, vol. 103. Springer, New York, pp. 209-224.
25. Leblanc F. Density estimation for a class of continuous time processes. Math. Methods Statist. 6 2 (1997) 171-199
26. Lepskii O.V. On a problem of adaptive estimation in Gaussian white noise. Theory Probab. Appl. 35 (1990) 454-466
27. Lepski O.V., Mammen E., and Spokoiny V.G. Optimal spatial adaptation to inhomogeneous smoothness. an approach based on kernel estimates with variable bandwidth selectors. Ann. Statist. 25 3 (1997) 929-947
28. McDiarmid, C., 1998. Concentration. Probabilistic Methods for Algorithmic Discrete Mathematics, vol. 16. Springer, Berlin, pp. 195-248.
29. Qian Z., Russo F., and Zheng W. Comparison theorem and estimates for transition probability densities of diffusion processes. Probab. Theory Related Fields 127 3 (2003) 388-406
30. Rio, E., 2000. Théorie asymptotique des processus aléatoires faiblements dépendants. Mathématiques & Applications, vol. 31. Springer, Berlin.
31. Sköld M. The asymptotic variance of the continuous-time kernel estimator with applications to bandwidth selection. Statist. Inference Stochastic Process. 4 1 (2001) 99-117
32. Sköld M. A bias correction for cross-validation bandwidth selection when a kernel estimate is based on dependent data. J. Time Ser. Anal. 22 4 (2001) 493-503
33. Sköld M., and Hössjer O. On the asymptotic variance of the continuous-time kernel density estimator. Statist. Probab. Lett. 44 1 (1999) 97-106
34. Stute W. The oscillation behavior of empirical processes: the multivariate case. Ann. Probab. 12 2 (1984) 361-379
35. p adaptive density estimation in a β mixing framework. Ann. Inst. H. Poincaré Probab. Statist. 34 2 (1998) 179-208
36. Veretennikov A.Y. On Castellana-Leadbetter's condition for diffusion density estimation. Statist. Inference Stochastic Process. 2 1 (1999) 1-9
37. Viano M.C., Deniau C., and Oppenheim G. Continuous-time fractional ARMA processes. Statist. Probab. Lett. 21 (1994) 323-336
38. Wu B. Kernel density estimation under weak dependence with sampled data. J. Statist. Plann. Inference 61 1 (1997) 141-154