Almost sure convergence of the kT-occupation time density estimator

Comptes Rendus Mathematique

Volumn 343, Issue 10, 2006, Pages 665-669

  Labrador, Boris ^a  

^a SORBONNE UNIVERSITÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33751106907     PISSN: 1631073X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.crma.2006.10.015     Document Type: Article

References (20)

1. Boente G., and Fraiman R. Strong order of convergence and asymptotic distribution of nearest neighbor density estimates from dependent observations. Sankhyā Ser. A 53 2 (1991) 194-205
2. Bosq D. Nonparametric Statistics for Stochastic Processes. Estimation and Prediction. Lecture Notes in Statist. second ed. vol. 110 (1998), Springer-Verlag, New York
3. Castellana J.V., and Leadbetter M.R. On smoothed probability density estimation for stationary processes. Stochastic Process. Appl. 21 (1986) 179-193
4. Chen X.-R. Convergence rates of nearest neighbor density estimates. Sci. Sinica Ser. A 25 5 (1982) 455-467
5. Deheuvels P., and Mason D.M. Functional laws of the iterated logarithm for the increments of empirical and quantile processes. Ann. Probab. 20 3 (1992) 1248-1287
6. Devroye L., and Penrod C.S. The strong uniform convergence of multivariate variable kernel estimates. Canad. J. Statist. 14 3 (1986) 211-219
7. Devroye L.P., and Wagner T.J. The strong uniform consistency of nearest neighbor density estimates. Ann. Statist. 5 3 (1977) 536-540
8. Doukhan P. Mixing. Properties and Examples. Lecture Notes in Statist. vol. 85 (1994), Springer-Verlag, New York
9. o 4, project No 21-49-004, USAF School of Aviation Medicine, Randolph Field, TX
10. Geman D., and Horowitz J. Occupation densities. Ann. Probab. 8 1 (1980) 1-67
11. Kutoyants Y.A. Statistical Inference for Ergodic Diffusion Processes. Springer Ser. Statist. (2003), Springer
12. Loftsgaarden D.O., and Quesenberry C.P. A nonparametric estimate of a multivariate density function. Ann. Math. Statist. 36 (1965) 1049-1051
13. Mack Y.P. Rate of strong uniform convergence of k-NN density estimates. J. Statist. Plann. Inference 8 2 (1983) 185-192
14. Moore D.S., and Henrichon E.G. Uniform consistency of some estimates of a density function. Ann. Math. Statist. 40 (1969) 1499-1502
15. Moore D.S., and Yackel J.W. Consistency properties of nearest neighbor density function estimators. Ann. Statist. 5 1 (1977) 143-154
16. Ralescu S.S. The law of the iterated logarithm for the multivariate nearest neighbor density estimators. J. Multivariate Anal. 53 1 (1995) 159-179
17. S. Levallois, PhD Thesis, University of Montpellier II, 1998
18. Tran L.T. On multivariate variable-kernel density estimates for time series. Canad. J. Statist. 19 4 (1991) 371-387
19. Wagner T.J. Strong consistency of nonparametric estimate of a density function. IEEE Trans. Systems Man Cybernet. 3 (1973) 289-290
20. Zhang D.-X. Rates of strong uniform convergence of nearest neighbor density estimates on any compact set. Appl. Math. Mech. 11 4 (1990) 385-393 (English ed.)