LAN in Problems of Nonparametric Estimation of Functions and Lower Bounds for Quadratic Risks

Previous article Next article LAN in Problems of Nonparametric Estimation of Functions and Lower Bounds for Quadratic RisksG. K. GolubevG. K. Golubevhttps://doi.org/10.1137/1136014PDFBibTexSections 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] B. Ya. Levit, Infinite-dimensional informational inequalities, Theory Probab. Appl., 23 (1978), 371–377 10.1137/1123040 0428.62051 LinkGoogle Scholar[3] P. Warwick Millar, The minimax principle in asymptotic statistical theoryEleventh Saint Flour probability summer school—1981 (Saint Flour, 1981), Lecture Notes in Math., Vol. 976, Springer, Berlin, 1983, 75–265 86d:62001 CrossrefGoogle Scholar[4] I. A. Ibragimov and , R. Z. 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Sz.-Nagy, Functional analysis, Frederick Ungar Publishing Co., New York, 1955xii+468, 2nd ed. 17,175i Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Efficient nonparametric estimation of distribution for current status censoringElectronic Journal of Statistics, Vol. 16, No. 1 | 1 Jan 2022 Cross Ref Minimax theory of nonparametric hazard rate estimation: efficiency and adaptationAnnals of the Institute of Statistical Mathematics, Vol. 68, No. 1 | 30 September 2014 Cross Ref Efficient shrinkage in parametric modelsJournal of Econometrics, Vol. 190, No. 1 | 1 Jan 2016 Cross Ref Minimax Risk, Pinsker Bound forWiley StatsRef: Statistics Reference Online | 29 September 2014 Cross Ref On shrinking minimax convergence in nonparametric statisticsJournal of Nonparametric Statistics, Vol. 26, No. 3 | 22 July 2014 Cross Ref An infinite dimensional convolution theorem with applications to the efficient estimation of the integrated volatilityStochastic Processes and their Applications, Vol. 123, No. 7 | 1 Jul 2013 Cross Ref Adaptivity and optimality of the monotone least-squares estimatorBernoulli, Vol. 17, No. 2 | 1 May 2011 Cross Ref Linear and convex aggregation of density estimatorsMathematical Methods of Statistics, Vol. 16, No. 3 | 1 Sep 2007 Cross Ref Sharp adaptive estimation of the drift function for ergodic diffusionsThe Annals of Statistics, Vol. 33, No. 6 | 1 Dec 2005 Cross Ref Nonparametric Sequential Minimax Estimation of the Drift Coefficient in Diffusion ProcessesSequential Analysis, Vol. 24, No. 3 | 1 Jul 2005 Cross Ref Density estimation for biased dataThe Annals of Statistics, Vol. 32, No. 3 | 1 Jun 2004 Cross Ref Estimation of Analytic Spectral Density of Gaussian Stationary ProcessesParametric and Semiparametric Models with Applications to Reliability, Survival Analysis, and Quality of Life | 1 Jan 2004 Cross Ref On second order minimax estimation of invariant density for ergodic diffusionStatistics & Decisions, Vol. 22, No. 1-2004 | 1 Jan 2004 Cross Ref Lower bounds for the asymptotic minimax risk with spherical dataJournal of Statistical Planning and Inference, Vol. 113, No. 1 | 1 Apr 2003 Cross Ref Density Estimation Under Random Censorship and Order RestrictionsJournal of the American Statistical Association, Vol. 96, No. 454 | 1 Jun 2001 Cross Ref Lower bound for quadratic losses of estimation of infinite-dimensional parameterLithuanian Mathematical Journal, Vol. 37, No. 1 | 1 Jan 1997 Cross Ref Asymptotic equivalence of density estimation and Gaussian white noiseThe Annals of Statistics, Vol. 24, No. 6 | 1 Dec 1996 Cross Ref On nonparametric regression for IID observations in a general settingThe Annals of Statistics, Vol. 24, No. 3 | 1 Jun 1996 Cross Ref Minimax Nonparametric Testing of Hypotheses on the Distribution DensityM. S. ErmakovTheory of Probability & Its Applications, Vol. 39, No. 3 | 17 July 2006AbstractPDF (1533 KB)Efficient nonparametric estimation of distribution density in the basis of algebraic polynomialsActa Applicandae Mathematicae, Vol. 38, No. 1 | 1 Jan 1995 Cross Ref Volume 36, Issue 1| 1992Theory of Probability & Its Applications1-208 History Submitted:18 July 1988Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1136014Article page range:pp. 152-157ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics