Convergence rates in nonparametric estimation of level sets

Statistics and Probability Letters

Volumn 53, Issue 1, 2001, Pages 27-35

  Baíllo, Amparo ^a   Cuesta Albertos, Juan A ^b   Cuevas, Antonio ^a  

^a UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

^b Estadistica Y Comp Univ C   (Spain)

Author keywords

Convergence rates; False alarm probability; Kernel density estimates; Level sets; Primary 62G05; Secondary 62G20; Set estimation

Indexed keywords

EID: 18044402908     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-7152(01)00006-2     Document Type: Article

References (18)

1. Baíllo, A., Cuevas, A., Justel, A., 2000. Set estimation and non-parametric detection. Canad. J. Statist. 28, 765-782.
2. Chanda K.C., Ruymgaart F.H. Asymptotic estimate of probability of misclassification for discriminant rules based on density estimates. Statist. Probab. Lett. 8:1989;81-88.
3. Choudhuri N. Bayesian bootstrap credible sets for multidimensional mean functional. Ann. Statist. 26:1999;2104-2127.
4. Cuevas A., Fraiman R. A plug-in approach to support estimation. Ann. Statist. 25:1997;2300-2312.
5. Cuevas A., Febrero M., Fraiman R. Estimating the number of clusters. Canad. J. Statist. 28:2000;367-382.
6. DasGupta A., Ghosh J.K., Zen M.M. A new general method for constructing confidence sets in arbitrary dimensions: with applications. Ann. Statist. 23:1995;1408-1432.
7. Davies L., Gather U. The identification of multiple outliers (with discussion). J. Amer. Statist. Assoc. 88:1993;782-801.
8. Devroye L., Wise G. Detection of abnormal behavior via nonparametric estimation of the support. SIAM J. Appl. Math. 38:1980;480-488.
9. Feller W. An Introduction to Probability Theory and Its Applications. 1968;Wiley, New York.
10. Hall P. On the law of logarithm for density estimators. Statist. Probab. Lett. 9:1990;237-240.
11. Hartigan J.A. Clustering Algorithms. 1975;Wiley, New York.
12. 1 error of a multivariate kernel density estimator J. Multivariate Anal. 42(2):1992;245-266.
13. Molchanov I.S. A limit theorem for solutions of inequalities. Scand. J. Statist. 25:1998;235-242.
14. Shiryayev A.N. Probability. 1984;Springer, Berlin.
15. Stute W. A law of the logarithm for kernel density estimators. Ann. Probab. 10(2):1982;414-422.
16. Stute W. The oscillation behavior of empirical processes: the multivariate case. Ann. Probab. 12(2):1984;361-379.
17. Tsybakov A.B. On nonparametric estimation of density level sets. Ann. Statist. 25:1997;948-969.
18. Wand M.P., Jones M.C. Kernel Smoothing. 1995;Chapman & Hall, London.