References
- Antoniadis , A. ( 1997 ). Wavelets in statistics: a review (with discussion) . J. Ital. Statist. Soc. Ser. B 6 : 97 – 144 .
- Butucea , C. , Matias , C. ( 2005 ). Minimax estimation of the noise level and of the signal density in a semiparametric convolution model . Bernoulli 11 ( 2 ): 309 – 340 .
- Caroll , R. J. , Hall , P. ( 1988 ). Optimal rates of convergence for deconvolving a density . J. Amer. Statist. Assoc. 83 : 1184 – 1186 .
- Chesneau , C. ( 2011 ). Adaptive wavelet estimator for a function and its derivatives in an indirect convolution model . J. Statist. Theor. Prac. 5 ( 2 ): 303 – 326 .
- Cohen , A. , Daubechies , I. , Jawerth , B. , Vial , P. ( 1993 ). Wavelets on the interval and fast wavelet transforms . Appl. Computat. Harmonic Anal. 24 ( 1 ): 54 – 81 .
- Comte , F. , Rozenholc , Y. , Taupin , M.-L. ( 2006 ). Penalized contrast estimator for density deconvolution . Can. J. Statist. 34 : 431 – 452 .
- Delaigle , A. , Gijbels , I. ( 2006 ). Estimation of boundary and discontinuity points in deconvolution problems . Statistica Sinica 16 : 773 – 788 .
- Delaigle , A. , Meister , A. ( 2008 ). Density estimation with heteroscedastic error . Bernoulli 14 : 562 – 579 .
- Devroye , L. ( 1989 ). Consistent deconvolution in density estimation . Can. J. Statist. 17 : 235 – 239 .
- Fan , J. ( 1991 ). On the optimal rates of convergence for nonparametric deconvolution problem . Ann. Statist. 19 : 1257 – 1272 .
- Fan , J. , Koo , J. Y. ( 2002 ). Wavelet deconvolution . IEEE Trans. Inform. Theor. 48 : 734 – 747 .
- Hall , P. , Qiu , P. ( 2005 ). Discrete-transform approach to deconvolution problems . Biometrika 92 : 135 – 148 .
- Hall , P. , Meister , A. ( 2007 ). A ridge-parameter approach to deconvolution . Ann. Statist. 35 : 1535 – 1558 .
- Härdle , W. , Kerkyacharian , G. , Picard , D. , Tsybakov , A. (1998). Wavelet, Approximation and Statistical Applications . Lectures Notes in Statistics. Vol. 129 . New York : Springer Verlag.
- Lacour , C. ( 2006 ). Rates of convergence for nonparametric deconvolution . Can. Roy. Acad. Sci. Paris Ser. I Math. 342 ( 11 ): 877 – 882 .
- Lounici , K. , Nickl , R. ( 2011 ). Global uniform risk bounds for wavelet deconvolution estimators . Ann. Statist. 39 : 201 – 231 .
- Mallat , S. ( 2009 ). A Wavelet Tour of Signal Processing . Elsevier/ Academic Press, Amsterdam . 3rd ed. The sparse way, with contributions from Gabriel Peyré .
- Meister , A. ( 2009 ). Deconvolution Problems in Nonparametric Statistics . Lecture Notes in Statistics . New York : Springer .
- Meister , A. , Stadtmüller , U. , Wagner , C. ( 2010 ). Density deconvolution in a two-level heteroscedastic model with unknown error density . Electron. J. Statist. 4 : 36 – 57 .
- Meyer , Y. ( 1992 ). Wavelets and Operators . Cambridge : Cambridge University Press .
- Pensky , M. , Vidakovic , B. ( 1999 ). Adaptive wavelet estimator for nonparametric density deconvolution . Ann. Statist. 27 : 2033 – 2053 .
- Pensky , M. , Sapatinas , T. ( 2010 ). On convergence rates equivalency and sampling strategies in functional deconvolution models . Ann. Statist. 38 ( 3 ): 1793 – 1844 .
- Staudenmayer , J. , Ruppert , D. , Buonaccorsi , J. ( 2008 ). Density estimation in the presence of heteroskedastic measurement error . JASA 103 : 726 – 736 .
- Tsybakov , A. ( 2004 ). Introduction à l'estimation Nonparamétrique . Berlin : Springer Verlag .
- Wang , X. F. , Fan , Z. , Wang , B. ( 2010 ). Estimating smooth distribution function in the presence of heterogeneous measurement errors . Computat. Statist. Data Anal. 54 : 25 – 36 .
- Wang , X. F. , Wang , B. ( 2011 ). Deconvolution estimation in measurement error models: The R package decon . J. Statist. Software 39 ( 10 ): 1 – 24 .
- Wavelab toolbox. http://www-stat.stanford.edu/~wavelab , 2001 .
- Zhang , S. , Karunamuni , R. ( 2000 ). Boundary bias correction for nonparametric deconvolution . Ann. Inst. Statist. Math. 52 : 612 – 629 .