Rates of strong uniform consistency for multivariate kernel density estimators

Annales de l'institut Henri Poincare (B) Probability and Statistics

Volumn 38, Issue 6, 2002, Pages 907-921

  Giné, Evarist ^a   Guillou, Armelle ^b  

^a UNIVERSITY OF CONNECTICUT   (United States)

^b SORBONNE UNIVERSITÉ   (France)

Author keywords

Kernel density estimators; Non parametric density estimation; Uniform almost sure rates

Indexed keywords

EID: 0036847557     PISSN: 02460203     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0246-0203(02)01128-7     Document Type: Article

References (16)

1. K. Alexander, Probability inequalities for empirical processes and a law of iterated logarithm, Ann. Probab. 12 (1984) 1041-1067.
2. P. Deheuvels, Uniform limit laws for kernel density estimators on possibly unbounded intervals, in: N. Limnios, M. Nikulin (Eds.), Recent Advances in Reliability Theory: Methodology, Practice and Inference, Birkhauser, Boston, 2000, pp. 477-492.
3. V. de la Peña, E. Giné, Decoupling, from Dependence to Independence, Springer-Verlag, New York, 1999.
4. R.M. Dudley, Uniform Central Limit Theorems, Cambridge University Press, Cambridge, UK, 1999.
5. U. Einmahl, D. Mason, Some universal results on the behavior of increments of partial sums, Ann. Probab. 24 (1996) 1388-1407.
6. U. Einmahl, D. Mason, An empirical process approach to the uniform consistency of kernel-type function estimators, J. Theoret. Probab. 13 (2000) 1-37.
7. E. Giné, A. Guillou, On consistency of kernel density estimators for randomly censored data: rates holding uniformly over adaptive intervals, Ann. Inst. Henri Poincaré - PR 37 (2001) 503-522.
8. E. Giné, V.I. Koltchinskii, J. Zinn, Weighted uniform consistency of kernel density estimators, Preprint, 2001.
9. P. Massart, Rates of convergence in the central limit theorem for empirical processes, Ann. Inst. Henri Poincaré 22 (1986) 381-423.
10. S.J. Montgomery-Smith, Comparison of sums of independent identically distributed random vectors, Probab. Math. Statist. 14 (1993) 281-285.
11. D. Nolan, D. Pollard, U-processes: rates of convergence, Ann. Statist. 15 (1987) 780-799.
12. M. Rosenblatt, Remarks on some nonparametric estimates of a density function, Ann. Math. Statist. 27 (1956) 832-835.
13. B.W. Silverman, Weak and strong uniform consistency of the kernel estimate of a density and its derivatives, Ann. Statist. 6 (1978) 177-189.
14. W. Stute, The oscillation behavior of empirical processes: the multivariate case, Ann. Probab. 12 (1984) 361-379.
15. M. Talagrand, Sharper bounds for Gaussian and empirical processes, Ann. Probab. 22 (1994) 28-76.
16. M. Talagrand, New concentration inequalities in product spaces, Invent. Math. 126 (1996) 505-563.