Invariance principles for deconvoluting kernel density estimation

References

• Carroll , R. J. and Hall , P. 1989 . Optimal rates of convergence for deconvoluting density . J. Amer. Statist. Assoc. , 83 : 1184 – 1186 .
   Google Scholar
• Csörgó , M. 1983 . Quantile Processes with Statistical Applications . CBM-NSF Regional Conference Series . 1983 . Vol. 42 , SIAM . In Applied Mathematics
   Google Scholar
• Csörgó , M. and Révész , P. 1981 . Strong approximations in probability and statistics , New York : Academic Press .
   Google Scholar
• Csörgó , M. , Csörgó , S. and Horváth , L. 1986 . An asymptotic theory for empirical reliability and concentration Processes , Vol. 33 , Berlin : Springer Verlag . Lecture Notes in Statistics
   Google Scholar
• Csörgó , M. and Horváth , L. 1993 . Weighted approximations in Probability and Statistics , New York : Wiley .
   Google Scholar
• Devroye , P. L. 1989 . Consistent deconvolution in density estimation . Canad. J. Statist. , 17 : 235 – 239 .
   Web of Science ®Google Scholar
• Fan , J. 1991 a . On the optimal rates of convergence for nonparametric deconvolution problems . Ann. Statist. , 19 : 1257 – 1272 .
   Web of Science ®Google Scholar
• Fan , J. 1991 b . Global behavior of deconvolution kernel estimates . Statist. Sinica , 1 : 541 – 551 .
   Web of Science ®Google Scholar
• Fan , J. 1992 . Deconvolution with supersmooth distributions . Canad. J. Statist. , 20 : 155 – 169 .
   Web of Science ®Google Scholar
• Fan , J. 1993 . Adaptively local one-dimensional subproblems with application to a deconvolution problem . Ann. Statist. , 21 : 600 – 610 .
   Web of Science ®Google Scholar
• 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 .
   Google Scholar
• 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
   Google Scholar
• James , B. R. 1975 . A functional law of the iterated logarithm for weighted empirical distributions . Ann. Probab , 14 : 278 – 292 .
   Google Scholar
• Gajek , L. 1989 . Estimating a density and its derivatives via the minimum distance method . Prob, Theory Rel. Fields , 80 : 601 – 617 .
   Google Scholar
• Hall , P. and Marron , J. S. 1988 . Variable window width kernel estimates of probability densities . Prob. Theory Rel. Fields , 80 : 37 – 49 .
   Web of Science ®Google Scholar
• Hoeffding , W. 1973 . On the centering of a simple linear rank statistic . Ann. Statist. , 1 : 54 – 66 .
   Web of Science ®Google Scholar
• 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 .
   Web of Science ®Google Scholar
• Liu , M. C. and Taylor , R. L. 1989 . A consistent nonparametric density estimator for the deconvolution problem . Canand. J. Statist. , 17 : 427 – 438 .
   Web of Science ®Google Scholar
• Nadaraya , E. A. 1974 . On the integral mean square error of some nonparametric estimates for the density function . Theory Prob. Appl. , 29 : 133 – 141 .
   Google Scholar
• Rosenblatt , M. 1991 . NSF-CBMS Regional Conference Series in Prob. and Statist . Stochastic curve estimation . 1991 . Vol. 3 ,
   Google Scholar
• Shorack , R. G. and Wellner , A. J. 1986 . Empirical processes with applications to statistics , New York : Wiley .
   Google Scholar
• Stefanski , L. A. and Carroll , R. J. 1990 . Deconvoluting kernel density estimators . Statistics , 21 : 169 – 184 .
   Google Scholar
• Zhang , C. H. 1990 . Fourier methods for estimating mixing density and distributions . Ann. Statist. , 18 : 809 – 830 .
   Google Scholar