On the asymptotlc normality for l₂-error of wavelei density estimator with application

References

• Bowman , A.W. 1982 . A Comparative study of some kernel-based nonparametric density estimates , Manchester-Sheffield of Probability and Statistics Research Report, 84/AWB/1 .
   Google Scholar
• Csorgo , M. and Horvath , L. 1988 . Central limit theorems for Lp-norms of density estimators . Probab. Theory Related Fields , 80 : 269 – 291 .
   Web of Science ®Google Scholar
• Delyon , B. and Judisky , A. 1996 . On Minimax Wavelet Estimators . Appl. Corn-put. Harmonic Analysis , 3 : 215 – 228 .
   Web of Science ®Google Scholar
• Donoho , D.L. , Johnstone , I.M. , Kerkyacharian , G. and Picard , D. 1996 . Density estimation by wavelet thresholding . Ann. Statist , 24 ( 2 ) : 508 – 539 .
   Web of Science ®Google Scholar
• Hall , P. 1984 . Central limit theorem for Integrated Square Error of Multivariate Nonparametric Density Estimators . J. Multivariate Anal , 14 ( 2 ) : 1 – 16 .
   Google Scholar
• Hall , P. and Patil , P. 1995 . Formulae for mean integrated error of nonlinear wavelet-based density estimators . Ann. Statist. , 23 ( 3 ) : 905 – 925 .
   Web of Science ®Google Scholar
• Horvath , L. 1991 . On the Lp-norms of multivariate density estimators . Ann. Statist , 19 ( 3 ) : 1933 – 1949 .
   Google Scholar
• Kerkyacharian , G. and Picard , D. 1992 . Density estimation in Besov space . Statist Probab. Letter , 13 ( 3 ) : 15 – 24 .
   Google Scholar
• Kerkyacharian , G. and Picard , D. 1993 . Density estimation by kernel and wavelet method; Optimality of Besov space . Statist Probab. Letter , 18 ( 3 ) : 327 – 336 .
   Google Scholar
• Masry , E. 1994 . Probability density estimation from dependent observations using wavelet orthonormal basis . Statist Probab. Letter , 21 ( 3 ) : 181 – 194 .
   Web of Science ®Google Scholar
• Nadaraya , E.A. 1989 . Nonparametric Estimation of Probability Density and Regression Curves , Dordrecht : Kluwer Academic Publisher .
   Google Scholar
• Walter , G.G. 1994 . Wavelets and other orthogonal systems with application , Boca Taton, Florida : CRC Press .
   Google Scholar
• Wu , D.W. 1996 . Asymptotic normality of the multiscale wavelet density estimator . Commun. Statist-Theory Meth , 25 ( 9 ) : 1957 – 1970 .
   Web of Science ®Google Scholar