On Nonparametric Estimation of the Value of a Linear Functional in Gaussian White Noise

Previous article Next article On Nonparametric Estimation of the Value of a Linear Functional in Gaussian White NoiseI. A. Ibragimov and R. Z. Khas’minskiiI. A. Ibragimov and R. Z. Khas’minskiihttps: //doi. org/10. 1137/1129002PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout1 I. A. Ibragimov and, R. Z. Khas'minskii, Some problems of nonparametric estimation of the value of a linear functional, Dokl. Akad. Nauk SSSR, 256 (1981), 781–783, (In Russian. ) 82g: 62059 0487. 62034 Google Scholar2 Ivar Ekeland and, Roger Temam, Convex analysis and variational problems, North-Holland Publishing Co. , Amsterdam, 1976ix+402, Elsevier 57: 3931b 0322. 90046 Google Scholar3 T. Bonnesen and, W. Fenchel, Theorie der konvexen Korper, Springer-Verlag, Berlin, 1934 0008. 07708 CrossrefGoogle Scholar4 L. Nirenberg, Topics in nonlinear functional analysis, Courant Institute of Mathematical Sciences New York University, New York, 1974viii+259 58: 7672 0286. 47037 Google Scholar5 K. Yoshida, Functional Analysis, Springer-Verlag, Berlin, 1965 CrossrefGoogle Scholar6 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 Scholar7 E. Lehmann, Testing statistical hypotheses, John Wiley edited by N. L. Johnson, Pergamon Press, New York, 1961xii+360 23: A1438 0112. 11105 Google Scholar9 I. S. Gradshteyn and, I. M. Ryzhik, Tables of Integrals, Series and Products, Academic Press, New York, 1965, revised Google Scholar10 I. L. Legostaeva and, A. N. Shiryaev, Minimax weights in a trend detection problem of a random process, Theory Prob. Appl. , 16 (1971), 344–349 0237. 62060 LinkGoogle Scholar11 G. Szegö, Orthogonal polynomials, American Mathematical Society, Providence, R. I. , 1978 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Augmented minimax linear estimationThe Annals of Statistics, Vol. 49, No. 6 | 1 Dec 2021 Cross Ref Estimating minimum effect with outlier selectionThe Annals of Statistics, Vol. 49, No. 1 | 1 Feb 2021 Cross Ref The Minimax Estimator of the Average Treatment Effect, among Linear Combinations of Conditional Average Treatment Effects EstimatorsSSRN Electronic Journal, Vol. 86 | 1 Jan 2021 Cross Ref Statistical Inference via Convex Optimization Nillas, Alice Anatoli Juditsky and Arkadi Nemirovski Princeton University Press, 2020, xiv + 656 pages, £ 70/85, hardcover ISBN: 978‐0‐6911‐9729‐6International Statistical Review, Vol. 88, No. 3 | 21 October 2020 Cross Ref Obtaining minimax lower bounds: a reviewJournal of the Korean Statistical Society, Vol. 49, No. 3 | 1 January 2020 Cross Ref Near-optimal recovery of linear and N-convex functions on unions of convex setsInformation and Inference: A Journal of the IMA, Vol. 9, No. 2 | 7 May 2019 Cross Ref Simple and honest confidence intervals in nonparametric regressionQuantitative Economics, Vol. 11, No. 1 | 1 January 2020 Cross Ref Optimized Regression Discontinuity DesignsThe Review of Economics and Statistics, Vol. 101, No. 2 | 1 May 2019 Cross Ref Minimax linear estimation at a boundary pointJournal of Multivariate Analysis, Vol. 165 | 1 May 2018 Cross Ref Simple and Honest Confidence Intervals in Nonparametric RegressionSSRN Electronic Journal | 1 Jan 2018 Cross Ref Simple and Honest Confidence Intervals in Nonparametric RegressionSSRN Electronic Journal | 1 Jan 2018 Cross Ref Optimal Inference in a Class of Regression ModelsSSRN Electronic Journal | 1 Jan 2017 Cross Ref Optimal Inference in a Class of Regression ModelsSSRN Electronic Journal | 1 Jan 2017 Cross Ref Minimax Linear Estimation at a Boundary PointSSRN Electronic Journal | 1 Jan 2017 Cross Ref ADAPTIVE ESTIMATION OF FUNCTIONALS IN NONPARAMETRIC INSTRUMENTAL REGRESSIONEconometric Theory, Vol. 32, No. 3 | 30 March 2015 Cross Ref Simple and Honest Confidence Intervals in Nonparametric RegressionSSRN Electronic Journal | 1 Jan 2016 Cross Ref Simple and Honest Confidence Intervals in Nonparametric RegressionSSRN Electronic Journal | 1 Jan 2016 Cross Ref Hypothesis testing by convex optimizationElectronic Journal of Statistics, Vol. 9, No. 2 | 1 Jan 2015 Cross Ref The Bayesian Analysis of Complex, High-Dimensional Models: Can It Be CODA? Statistical Science, Vol. 29, No. 4 | 1 Nov 2014 Cross Ref On estimation of analytic density functions in L pMathematical Methods of Statistics, Vol. 22, No. 2 | 27 June 2013 Cross Ref On rate optimal local estimation in functional linear regressionElectronic Journal of Statistics, Vol. 7, No. none | 1 Jan 2013 Cross Ref Adaptive estimation of linear functionals in functional linear modelsMathematical Methods of Statistics, Vol. 21, No. 3 | 27 September 2012 Cross Ref Minimax signal detection in ill-posed inverse problemsThe Annals of Statistics, Vol. 40, No. 3 | 1 Jun 2012 Cross Ref Minimax revisited. IIMathematical Methods of Statistics, Vol. 19, No. 4 | 6 January 2011 Cross Ref Estimating Divergence Functionals and the Likelihood Ratio by Convex Risk MinimizationIEEE Transactions on Information Theory, Vol. 56, No. 11 | 1 Nov 2010 Cross Ref Minimax revisited. IMathematical Methods of Statistics, Vol. 19, No. 3 | 3 October 2010 Cross Ref Weyl eigenvalue asymptotics and sharp adaptation on vector bundlesJournal of Multivariate Analysis, Vol. 100, No. 9 | 1 Oct 2009 Cross Ref Minimax estimation of linear functionals under squared error lossJournal of Statistical Planning and Inference, Vol. 139, No. 9 | 1 Sep 2009 Cross Ref Nonparametric statistical inverse problemsInverse Problems, Vol. 24, No. 3 | 23 May 2008 Cross Ref Empirical bayesian test of the smoothnessMathematical Methods of Statistics, Vol. 17, No. 1 | 7 June 2008 Cross Ref Sharp adaptation for spherical inverse problems with applications to medical imagingJournal of Multivariate Analysis, Vol. 99, No. 2 | 1 Feb 2008 Cross Ref Uniform and individual convergence rates for convex density classesStatistics & Decisions, Vol. 26, No. 1 | 1 Jan 2008 Cross Ref Sharp adaptive estimation of quadratic functionalsProbability Theory and Related Fields, Vol. 134, No. 4 | 6 June 2005 Cross Ref Asymptotically efficient estimation of linear functionals in inverse regression modelsJournal of Nonparametric Statistics, Vol. 17, No. 7 | 1 Oct 2005 Cross Ref On adaptive estimation of linear functionalsThe Annals of Statistics, Vol. 33, No. 5 | 1 Oct 2005 Cross Ref Minimax expected measure confidence sets for restricted location parametersBernoulli, Vol. 11, No. 4 | 1 Aug 2005 Cross Ref Block thresholding for density estimation: local and global adaptivityJournal of Multivariate Analysis, Vol. 95, No. 1 | 1 Jul 2005 Cross Ref Nonparametric estimation over shrinking neighborhoods: Superefficiency and adaptationThe Annals of Statistics, Vol. 33, No. 1 | 1 Feb 2005 Cross Ref An adaptation theory for nonparametric confidence intervalsThe Annals of Statistics, Vol. 32, No. 5 | 1 Oct 2004 Cross Ref Exact constants for pointwise adaptive estimation under the Riesz transformProbability Theory and Related Fields, Vol. 129, No. 3 | 29 April 2004 Cross Ref Minimax estimation of linear functionals over nonconvex parameter spacesThe Annals of Statistics, Vol. 32, No. 2 | 1 Apr 2004 Cross Ref A note on nonparametric estimation of linear functionalsThe Annals of Statistics, Vol. 31, No. 4 | 1 Aug 2003 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 Recovering edges in ill-posed inverse problems: optimality of curvelet framesThe Annals of Statistics, Vol. 30, No. 3 | 1 Jun 2002 Cross Ref Estimating monotone functionsStatistics & Probability Letters, Vol. 56, No. 4 | 1 Feb 2002 Cross Ref Sharp Adaptive Estimation of Linear FunctionalsThe Annals of Statistics, Vol. 29, No. 6 | 1 Dec 2001 Cross Ref CHARACTERISATION OF LINEAR MINI-MAX ESTIMATORS FOR LOSS FUNCTIONS OF ARBITRARY POWERInternational Game Theory Review, Vol. 03, No. 02n03 | 1 Jun 2001 Cross Ref Minimax Risk Bounds in Extreme Value TheoryThe Annals of Statistics, Vol. 29, No. 1 | 1 Feb 2001 Cross Ref Minimax recovery of blurred signal from discrete noisy dataJournal of Nonparametric Statistics, Vol. 13, No. 5 | 1 Jan 2001 Cross Ref Efficient estimation of a density in a problem of tomographyThe Annals of Statistics, Vol. 28, No. 2 | 1 Apr 2000 Cross Ref Asymptotic Efficiency of Inverse EstimatorsTheory of Probability & Its Applications, Vol. 44, No. 4 | 25 July 2006AbstractPDF (190 KB) Pointwise and sup-norm sharp adaptive estimation of functions on the Sobolev classesThe Annals of Statistics, Vol. 26, No. 6 | 1 Dec 1998 Cross Ref Minimax linear estimation in a white noise problemThe Annals of Statistics, Vol. 25, No. 2 | 1 Apr 1997 Cross Ref Computing Linear Mini-Max EstimatorsGame Theoretical Applications to Economics and Operations Research | 1 Jan 1997 Cross Ref A constrained risk inequality with applications to nonparametric functional estimationThe Annals of Statistics, Vol. 24, No. 6 | 1 Dec 1996 Cross Ref Adaptive estimates of linear functionalsProbability Theory and Related Fields, Vol. 98, No. 2 | 1 Jun 1994 Cross Ref Minimaxity, More or LessStatistical Decision Theory and Related Topics V | 1 Jan 1994 Cross Ref On Minimax RiskTheory of Probability & Its Applications, Vol. 35, No. 1 | 17 July 2006AbstractPDF (573 KB) On Minimax Estimation of RegressionTheory of Probability & Its Applications, Vol. 35, No. 3 | 17 July 2006AbstractPDF (1287 KB) Functional version of the delta method and its applicationCommunications in Statistics - Theory and Methods, Vol. 20, No. 1 | 27 June 2007 Cross Ref Optimal nonparametric estimation for some semimartingale stochastic differential equationsApplied Mathematics and Computation, Vol. 39, No. 3 | 1 Oct 1990 Cross Ref Optimal nonparametric estimation for some semimartingale stochastic differential equationsApplied Mathematics and Computation, Vol. 37, No. 3 | 1 Jun 1990 Cross Ref Volume 29, Issue 1| 1985Theory of Probability & Its Applications1-204 History Submitted: 27 July 1982Published online: 17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI: 10. 1137/1129002Article page range: pp. 18-32ISSN (print): 0040-585XISSN (online): 1095-7219Publisher: Society for Industrial and Applied Mathematics