Invariance principles for deconvoluting kernel density estimation

Journal of Nonparametric Statistics

Volumn 7, Issue 2, 1996, Pages 155-170

  Fotopoulos, Stergios B ^a  

^a WASHINGTON STATE UNIVERSITY   (United States)

Author keywords

Deconvolution; Nonparametric Density Estimator; Smoothness of Error Distribution

Indexed keywords

EID: 0042043042     PISSN: 10485252     EISSN: None     Source Type: Journal    
DOI: 10.1080/10485259608832696     Document Type: Article

References (23)

1. Carroll, R. J. and Hall, P. (1989). Optimal rates of convergence for deconvoluting density. J. Amer. Statist. Assoc., 83, 1184-1186.
2. Csörgó M. (1983). Quantile Processes with Statistical Applications. CBM-NSF Regional Conference Series In Applied Mathematics SIAM Vol.42.
3. Csörgó, M. and Révész, P. (1981). Strong approximations in probability and statistics. Academic Press, New York.
4. Csörgó, M. Csörgó, S. and Horváth, L. (1986). An asymptotic theory for empirical reliability and concentration Processes. Lecture Notes in Statistics, 33, Springer Verlag, Berlin.
5. Csörgó, M. and Horváth, L. (1993). Weighted approximations in Probability and Statistics. Wiley, New York.
6. Devroye, P. L. (1989). Consistent deconvolution in density estimation. Canad. J. Statist., 17, 235-239.
7. Fan, J. (1991a). On the optimal rates of convergence for nonparametric deconvolution problems. Ann. Statist., 19, 1257-1272.
8. Fan, J. (1991b). Global behavior of deconvolution kernel estimates. Statist. Sinica., 1, 541-551.
9. Fan, J. (1992). Deconvolution with supersmooth distributions. Canad. J. Statist., 20, 155-169.
10. Fan, J. (1993). Adaptively local one-dimensional subproblems with application to a deconvolution problem. Ann. Statist., 21, 600-610.
11. Fotopoulos, S. B., Cho, S. and Ahn, S. (1993). Deviations between sample quantiles and empirical processes under absolute regular properties. J. Nonpar. Statist., 2, 225-234.
12. Fotopoulos, S. B., Ahn, S. and Cho, S. (1994). Strong approximation of the quantile processes and its applications under strong properties. J. Multiv. Analysis, 49, to appear.
13. James, B. R. (1975). A functional law of the iterated logarithm for weighted empirical distributions. Ann. Probab., 14, 278-292.
14. Gajek, L. (1989). Estimating a density and its derivatives via the minimum distance method. Prob, Theory Rel. Fields, 80, 601-617.
15. Hall, P. and Marron, J. S. (1988). Variable window width kernel estimates of probability densities. Prob. Theory Rel. Fields, 80, 37-49.
16. Hoeffding, W. (1973). On the centering of a simple linear rank statistic. Ann. Statist., 1, 54-66.
17. Komlös, J., Major, P. and Tusnády, G. (1975). An approximation of partial sums of independent random variables and the sample density function. I. Z. Wahrschein. Verb. Geb., 32, 111-131.
18. Liu, M. C. and Taylor, R. L. (1989). A consistent nonparametric density estimator for the deconvolution problem. Canand. J. Statist., 17, 427-438.
19. Nadaraya, E. A. (1974). On the integral mean square error of some nonparametric estimates for the density function. Theory Prob. Appl., 29, 133-141.
20. Rosenblatt, M. (1991). Stochastic curve estimation. NSF-CBMS Regional Conference Series in Prob. and Statist., Vol. 3.
21. Shorack, R. G. and Wellner, A. J. (1986). Empirical processes with applications to statistics. Wiley, New York.
22. Stefanski, L. A. and Carroll, R. J. (1990). Deconvoluting kernel density estimators. Statistics, 21, 169-184.
23. Zhang, C. H. (1990). Fourier methods for estimating mixing density and distributions. Ann. Statist., 18, 809-830.