Nonparametric Estimation of a Density of Unknown Smoothness

Previous article Next article Nonparametric Estimation of a Density of Unknown SmoothnessS. Yu. EfroimovichS. Yu. Efroimovichhttps://doi.org/10.1137/1130067PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] I. A. Ibragimov and , R. Z. Khas'minskii, Statistical estimation, Applications of Mathematics, Vol. 16, Springer-Verlag, New York, 1981vii+403, Asymptotic Theory 82g:62006 0467.62026 CrossrefGoogle Scholar[2] N. N. Chentsov, Statistical Decision Rules and Optimum Inference, American Math. Society, Providence, 1980 Google Scholar[3] Murray Rosenblatt, Remarks on some nonparametric estimates of a density function, Ann. Math. Statist., 27 (1956), 832–837 18,159f 0073.14602 CrossrefGoogle Scholar[4] E. A. Nadaraya, On nonparametric estimates of density functions and regression curves, Theory Prob. Appl., 10 (1965), 186–190 LinkGoogle Scholar[5] V. N. Vapnik and , A. R. Stefanyuk, Nonparametric methods for reconstructing density functions, Avtomat. i Telemekh., 8 (1978), 38–52, (In Russian.) Google Scholar[6] R. Yu. Bentkus and , A. R. Kazbaras, On optimal statistical estimators of a distribution density, Soviet Math. Dokl., 23 (1981), 487–490, (In Russian.) 0501.62027 Google Scholar[7] S. Yu. Efroimovich and , M. S. Pinsker, Estimation of square-integrable probability density of a random variable, Problemy Peredachi Informatsii, 18 (1982), 19–38, (In Russian.) 85c:62093 Google Scholar[8] K. V. Bondarenko, On a minimax bound of the L₂-risk in estimating analytic densities, Theory Prob. Appl., 27 (1982), 210– Google Scholar[9] M. S. Pinsker, Optimal filtering of functions in L₂ on a background of Gaussian noise, Problemy Peredachi Informatsii, 16 (1980), 52–68, (In Russian.) 0452.94003 Google Scholar[10] S. Yu. Efroimovich and , M. S. 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