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 SectionsAbout[1] 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 Scholar[2] Ivar Ekeland and , Roger Temam, Convex analysis and variational problems, North-Holland Publishing Co., Amsterdam, 1976ix+402, Elsevier 57:3931b 0322.90046 Google Scholar[3] T. Bonnesen and , W. Fenchel, Theorie der konvexen Korper, Springer-Verlag, Berlin, 1934 0008.07708 CrossrefGoogle Scholar[4] L. Nirenberg, Topics in nonlinear functional analysis, Courant Institute of Mathematical Sciences New York University, New York, 1974viii+259 58:7672 0286.47037 Google Scholar[5] K. Yoshida, Functional Analysis, Springer-Verlag, Berlin, 1965 CrossrefGoogle Scholar[6] 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[7] E. Lehmann, Testing statistical hypotheses, John Wiley & Sons Inc., New York, 1959xiii+369 21:6654 0089.14102 Google Scholar[8] Yu. V. Linnik, Method of least squares and principles of the theory of observations., Translated from the Russian by Regina C. Elandt; edited by N. L. Johnson, Pergamon Press, New York, 1961xii+360 23:A1438 0112.11105 Google Scholar[9] I. S. Gradshteyn and , I. M. Ryzhik, Tables of Integrals, Series and Products, Academic Press, New York, 1965, revised Google Scholar[10] 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 Scholar[11] 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