Some Problems on Nonparametric Estimation in Gaussian White Noise

Previous article Next article Some Problems on Nonparametric Estimation in Gaussian White NoiseI. A. Ibragimov, A. S. Nemirovskii, and R. Z. Khas’minskiiI. A. Ibragimov, A. S. Nemirovskii, and R. Z. Khas’minskiihttps: //doi. org/10. 1137/1131054PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout1 A. Kolmogoroff, Über die beste Annäherung von Funktionen einer gegebenen Funktionenklasse, Ann. of Math. (2), 37 (1936), 107–110 1 503 273 0013. 34903 CrossrefGoogle Scholar2 V. Tikhomirov, Some Questions in Approximation Theory, Moscow St. Univ. , Moscow, 1976, (In Russian. ) Google Scholar3 I. A. Ibragimov and, R. Z. Khas'minskii, Statistical estimation, Applications of Mathematics, Vol. 16, Springer-Verlag, New York, 1981vii+403, Asymptotic Theory, Berlin–Heidelberg 82g: 62006 0467. 62026 CrossrefGoogle Scholar4 I. A. Ibragimov and, R. Z. Khas'minskii, A problem of statistical estimation in Gaussian white noise, Soviet Math. 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Chentsov, Statistical Decision Rules and Optimal Inference, American Mathematical Society, Providence, RI, 1980 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Minimax Off-Policy Evaluation for Multi-Armed BanditsIEEE Transactions on Information Theory, Vol. 68, No. 8 | 1 Aug 2022 Cross Ref Estimation of smooth functionals in normal models: Bias reduction and asymptotic efficiencyThe Annals of Statistics, Vol. 49, No. 5 | 1 Oct 2021 Cross Ref Estimation of Smooth Functionals of Location Parameter in Gaussian and Poincaré Random Shift ModelsSankhya A, Vol. 83, No. 2 | 9 January 2021 Cross Ref Efficient estimation of smooth functionals in Gaussian shift modelsAnnales de l'Institut Henri Poincaré, Probabilités et Statistiques, Vol. 57, No. 1 | 1 Feb 2021 Cross Ref Optimal rates of entropy estimation over Lipschitz ballsThe Annals of Statistics, Vol. 48, No. 6 | 1 Dec 2020 Cross Ref Estimating linear and quadratic forms via indirect observationsBernoulli, Vol. 26, No. 4 | 1 Nov 2020 Cross Ref Chebyshev polynomials, moment matching, and optimal estimation of the unseenThe Annals of Statistics, Vol. 47, No. 2 | 1 Apr 2019 Cross Ref Smart Detection of Line-Search Oracle AttacksIEEE Transactions on Information Forensics and Security, Vol. 12, No. 3 | 1 Mar 2017 Cross Ref Minimax Rates of Entropy Estimation on Large Alphabets via Best Polynomial ApproximationIEEE Transactions on Information Theory, Vol. 62, No. 6 | 1 Jun 2016 Cross Ref Estimation of functionals of sparse covariance matricesThe Annals of Statistics, Vol. 43, No. 6 | 1 Dec 2015 Cross Ref Optimal entropy estimation on large alphabets via best polynomial approximation2015 IEEE International Symposium on Information Theory (ISIT) | 1 Jun 2015 Cross Ref Minimax and Adaptive Inference in Nonparametric Function EstimationStatistical Science, Vol. 27, No. 1 | 1 Feb 2012 Cross Ref Deconvolution on the Euclidean motion group SE (3) Inverse Problems, Vol. 27, No. 3 | 16 February 2011 Cross Ref Semiparametric Regression with Kernel Error ModelScandinavian Journal of Statistics, Vol. 0, No. 0 | 19 March 2007 Cross Ref Sharp adaptive estimation of quadratic functionalsProbability Theory and Related Fields, Vol. 134, No. 4 | 6 June 2005 Cross Ref Semiparametric Regression with Kernel Error ModelSSRN Electronic Journal | 1 Jan 2006 Cross Ref Nonquadratic estimators of a quadratic functionalThe Annals of Statistics, Vol. 33, No. 6 | 1 Dec 2005 Cross Ref Near-Optimal Detection of Geometric Objects by Fast Multiscale MethodsIEEE Transactions on Information Theory, Vol. 51, No. 7 | 1 Jul 2005 Cross Ref Adaptive estimation of a quadratic functional of a density by model selectionESAIM: Probability and Statistics, Vol. 9 | 15 November 2005 Cross Ref On nonparametric tests of positivity/monotonicity/convexityThe Annals of Statistics, Vol. 30, No. 2 | 1 Apr 2002 Cross Ref Structure Adaptive Approach for Dimension ReductionThe Annals of Statistics, Vol. 29, No. 6 | 1 Dec 2001 Cross Ref On Testing a Hypothesis Which Is Close to a Simple HypothesisTheory of Probability & Its Applications, Vol. 45, No. 2 | 25 July 2006AbstractPDF (194 KB) Estimating functionals, IILectures on Probability Theory and Statistics | 2 May 2007 Cross Ref Wavelet methods to estimate an integrated quadratic functional: Adaptivity and asymptotic lawStatistics & Probability Letters, Vol. 44, No. 2 | 1 Aug 1999 Cross Ref Estimation Problems for Coefficients of Stochastic Partial Differential Equations. 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