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 SectionsAbout1 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 Scholar2 N. N. Chentsov, Statistical Decision Rules and Optimum Inference, American Math. Society, Providence, 1980 Google Scholar3 Murray Rosenblatt, Remarks on some nonparametric estimates of a density function, Ann. Math. Statist. , 27 (1956), 832–837 18, 159f 0073. 14602 CrossrefGoogle Scholar4 E. A. Nadaraya, On nonparametric estimates of density functions and regression curves, Theory Prob. Appl. , 10 (1965), 186–190 LinkGoogle Scholar5 V. N. Vapnik and, A. R. Stefanyuk, Nonparametric methods for reconstructing density functions, Avtomat. i Telemekh. , 8 (1978), 38–52, (In Russian. ) Google Scholar6 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 Scholar7 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 Scholar8 K. V. Bondarenko, On a minimax bound of the L₂-risk in estimating analytic densities, Theory Prob. Appl. , 27 (1982), 210– Google Scholar9 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 Scholar10 S. Yu. Efroimovich and, M. S. 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