On a Plug-In Wavelet Estimator for Convolutions of Densities

References

• Ahmad, I. A., and Y. Fan. 2001. Optimal bandwidth for kernel density estimators of functions of observations. Stat. Prob. Lett., 51, 245–251.
   Web of Science ®Google Scholar
• Ahmad, I. A., and A. R. Mugdadi. 2003. Analysis of kernel density estimation of functions of random variables. J. Nonparametric Stat., 15, 579–605.
   Web of Science ®Google Scholar
• Antoniadis, A. 1997. Wavelets in statistics: A review (with discussion). J. Ital. Stat. Soc. Ser. B, 6, 97–144.
   Google Scholar
• Butucea, C., and C. Matias. 2005. Minimax estimation of the noise level and of the deconvolution density in a semiparametric convolution model. Bernoulli, 11, 309–340.
   Web of Science ®Google Scholar
• Cai, T. 1999. Adaptive wavelet estimation: A block thresholding and oracle inequality approach. Ann. Stat., 27, 898–924.
   Web of Science ®Google Scholar
• Caroll, R. J., and P. Hall. 1988. Optimal rates of convergence for deconvolving a density. J. Am. Stat. Assoc., 83, 1184–1186.
   Web of Science ®Google Scholar
• Chesneau, C. 2008. Wavelet estimation via block thresholding: A minimax study under risk. Stat. Sin., 18, 1007–1024.
   Web of Science ®Google Scholar
• Chesneau, C., M. J. Fadili, and J.-L. Starck. 2010. Stein block thresholding for image denoising. Appl. Comput. Harmonic Anal., 28, 67–88.
   Web of Science ®Google Scholar
• Cohen, A., I., Daubechies, B. Jawerth, and P. Vial. 1993. Wavelets on the interval and fast wavelet transforms. Appl. Comput. Harmonic Anal., 24, 54–81.
   Google Scholar
• Comte, F., Y. Rozenholc, and M.-L. Taupin. 2006. Penalized contrast estimator for adaptive density deconvolution. Can. J. Stat., 34, 431–452.
   Web of Science ®Google Scholar
• Delaigle, A., and I. Gijbels. 2006. Estimation of boundary and discontinuity points in deconvolution problems. Stat. Sin., 16, 773–788.
   Web of Science ®Google Scholar
• Donoho, D., I. Johnstone, G. Kerkyacharian, and D. Picard. 1996. Density estimation by wavelet thresholding. Ann. Stat., 24, 508–539.
   Web of Science ®Google Scholar
• Du, J., and A. Schick. 2007. Root-n consistency and functional central limit theorems for estimators of derivatives of convolutions of densities. Int. J. Stat. Manage. Systems, 2, 67–87.
   Google Scholar
• Fan, J. 1991. On the optimal rates of convergence for nonparametric deconvolution problem. Ann. Stat., 19, 1257–1272.
   Web of Science ®Google Scholar
• Fan, J. and Y. Liu. 1997. A note on asymptotic normality for deconvolution kernel density estimators. Sankhya, 59, 138–141.
   Google Scholar
• Fan, J., and J. Y. Koo. 2002. Wavelet deconvolution. IEEE Trans. Information Theory, 48, 734–747.
   Web of Science ®Google Scholar
• Frees, E. 1994. Estimating densities of functions of observations. J. Am. Stat. Assoc., 89, 517–525.
   Web of Science ®Google Scholar
• Giné, E., and D. M. Mason. 2007. On local U-statistic processes and the estimation of densities of functions of several sample variables. Ann. Stat., 35, 1105–1145.
   Web of Science ®Google Scholar
• Härdle, W., G. Kerkyacharian, D. Picard, and A. Tsybakov. 1998. Wavelet, approximation and statistical applications. Lectures Notes in Statistics, 129. New York, NY: Springer Verlag.
   Google Scholar
• Kerkyacharian, G., and D. Picard. 2000. Thresholding algorithms, maxisets and well concentrated bases (with discussion and a rejoinder by the authors). Test, 9, 283–345.
   Web of Science ®Google Scholar
• Lacour, C. 2006. Rates of convergence for nonparametric deconvolution. C. R. Acad. Sci. Paris Ser. I Math., 342 (11), 877–882.
   Google Scholar
• Mallat, S. 2009. A wavelet tour of signal processing, The Sparse way, 3rd ed., with contributions from Gabriel Peyré. Amsterdam, The Netherlands: Elsevier/Academic Press.
   Google Scholar
• Marron, J. S., and M. P. Wand. 1992. Exact mean integrated squared error. Ann. Stat., 20, 712–736.
   Web of Science ®Google Scholar
• Meyer, Y. 1992. Wavelets and operators. Cambridge, UK: Cambridge University Press.
   Google Scholar
• Mugdadi, A. R., and I. Ahmad. 2004. A bandwidth selection for kernel density estimation of functions of random variables. Comput. Stat. Data Anal., 47, 49–62.
   Web of Science ®Google Scholar
• Panjer, H. H., and G. E. Willmot. 1992. Insurance risk models. Schaumburg, Germany: Society of Actuaries.
   Google Scholar
• Pensky, M., and B. Vidakovic. 1999. Adaptive wavelet estimator for nonparametric density deconvolution. Ann. Stat., 27, 2033–2053.
   Web of Science ®Google Scholar
• Prakasa Rao, B. L. S. 2004. Moment inequalities for supremum of empirical processes of U-statistic structure and application to density estimation. J. Iran. Stat. Soc., 3, 59–68.
   Google Scholar
• Saavedra, A., and R. Cao. 2000. On the estimation of the marginal density of a moving average process. Can. J. Stat., 28, 799–815.
   Web of Science ®Google Scholar
• Silverman, B. W. 1986. Density estimation: For statistics and data analysis. London, UK: Chapman and Hall.
   Google Scholar
• Schick, A., and W. Wefelmeyer. 2004. Root n consistent density estimators for sums of independent random variables. J. Nonparametric Stat., 16, 925–935.
   Web of Science ®Google Scholar
• Schick, A., and W. Wefelmeyer. 2007. Root n consistent density estimators of convolutions in weighted -norms. J. Stat. Plann. Inference, 137, 1765–1774.
   Web of Science ®Google Scholar
• Tsybakov, A. 2004. Introduction à l’estimation nonparamétrique. Berlin, Germany: Springer Verlag.
   Google Scholar
• Vidakovic, B. 1999. Statistical modeling by wavelets. New York, NY: John Wiley & Sons.
   Google Scholar