Asymptotically Minimax Adaptive Estimation. I: Upper Bounds. Optimally Adaptive Estimates

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Previous article Next article Asymptotically Minimax Adaptive Estimation. I: Upper Bounds. Optimally Adaptive EstimatesO. V. LepskiiO. V. Lepskiihttps://doi.org/10.1137/1136085PDFBibTexSections 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] S. Yu. Efroimovich and , M. S. Pinsker, A self-educating nonparametric filtration algorithm, Automation and Remote Control, 45 (1984), 58–65 Google Scholar[3] Charles J. Stone, Optimal global rates of convergence for nonparametric regression, Ann. Statist., 10 (1982), 1040–1053 84b:62058 0511.62048 CrossrefGoogle Scholar[4] W. Hardle and , J. S. Marron, Optimal bandwidth selection in nonparametric regression function estimation, Ann. Statist., 13 (1985), 1465–1481 87b:62047 CrossrefGoogle Scholar[5] S. Yu. Efroimovich, Nonparametric estimation of a density of unknown smoothness, Theory Probab. Appl., 30 (1985), 557–561 10.1137/1130067 LinkGoogle Scholar[6] I. A. Ibragimov and , R. Z. Khas'minskii, Estimates of the signal, its derivatives and point of maximum for Gaussian distributions, Theory Probab. Appl., 25 (1980), 703–718 10.1137/1125086 0471.60050 LinkGoogle Scholar[7] O. V. Lepskii, On a problem of adaptive estimation in Gaussian white noise, Theory Probab. Appl., 35 (1990), 454–466 10.1137/1135065 LinkGoogle Scholar[8] A. P. Korostelev and , O. V. Lepskii, Minimax estimation of the prediction length for a polynomial trendStatistical Methods and Models, VNIISI, Moscow, 1987, 52–59, (In Russian.) Google Scholar[9] V. V. Godovanchuk and , A. P. Korostelev, Conditions for local convergence of recursive stochastic procedures, Theory Probab. Appl., 28 (1983), 142–149 10.1137/1128009 LinkGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Minimax estimation of norms of a probability density: II. 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II. Schemes without Optimal Adaptation: Adaptive EstimatorsO. V. LepskiiTheory of Probability & Its Applications, Vol. 37, No. 3 | 17 July 2006AbstractPDF (1226 KB) Volume 36, Issue 4| 1992Theory of Probability & Its Applications647-859 History Submitted:12 October 1988Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1136085Article page range:pp. 682-697ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics