On Minimax Estimation of Regression
Iosif F Pinelis · Theory of Probability and Its Applications · 1991
Previous article Next article On Minimax Estimation of RegressionI. F. PinelisI. F. Pinelishttps://doi.org/10.1137/1135069PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Yu. A. Rozanov, On a new class of estimatesMultivariate Analysis, II (Proc. Second Internat. Sympos., Dayton, Ohio, 1968), Academic Press, New York, 1969, 437–441 44:1173 Google Scholar[2] I. A. Ibragimov and , R. Z. Khas'minskii, On nonparametric estimation of the value of linear functionals in Gaussian white noise, Theory Probab. Appl., 29 (1984), 18–32 10.1137/1129002 0575.62076 LinkGoogle Scholar[3] I. A. Ibragimov and , R. Z. Khas'minskii, Estimation of linear functionals in Gaussian noise, Theory Probab. Appl., 32 (1987), 30–39 10.1137/1132002 0678.62080 LinkGoogle Scholar[4] A. M. Fedotov and , O. V. Levchuk, Optimal estimates of linear functionals in solutions of operator equations of the first kind with random errors in data, Soviet Math. Dokl., 287 (1986), 63–66, (In Russian.) Google Scholar[5] R. D. Dodunekova and , R. Z. Khas'minskii, Estimates of values of a linear functional from indirect observations, Probl. Inform. Transmission, 23 (1987), 54–60 Google Scholar[6] Alexander M. Samarov, Robust spectral regression, Ann. Statist., 15 (1987), 99–111 89b:62197 0644.62095 CrossrefGoogle Scholar[7] I. F. Pinelis, An approach to minimax theorems, First World Congress of the Bernoulli Society on Mathematical Statistics and Theory of Probability, Theses, Vol. II, Nauka, Moscow, 1986, 902– Google Scholar[8] I. F. Pinelis, On minimax risk, Theory Probab. Appl., 35 (1990), 104–109 10.1137/1135010 0711.62008 LinkGoogle Scholar[9] Ivar Ekeland and , Roger Temam, Convex analysis and variational problems, North-Holland Publishing Co., Amsterdam, 1976ix+402 57:3931b 0322.90046 Google Scholar[10] Albert W. Marshall and , Ingram Olkin, Inequalities: theory of majorization and its applications, Mathematics in Science and Engineering, Vol. 143, Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York, 1979xx+569, London 81b:00002 0437.26007 Google Scholar[11] Yu. A. Rozanov and , M. V. Kozlov, On asymptotically efficient estimation of regression coefficients, Soviet Math. Dokl., 188 (1969), 1075–1078 0206.20001 Google Scholar[12] I. A. Ibragimov and , Yu. A. Rozanov, Gaussian random processes, Applications of Mathematics, Vol. 9, Springer-Verlag, New York, 1978x+275, Berlin, Heidelberg 80f:60038 0392.60037 CrossrefGoogle Scholar[13] K. Yosida, Functional analysis, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Vol. 123, Springer-Verlag, Berlin, 1980xii+501, 6th ed., Heidelberg 82i:46002 0435.46002 CrossrefGoogle Scholar[14] V. L. Levin, Convex Analysis in Spaces of Measurable Functions and Its Applications in Mathematics and Economics, Nauka, Moscow, 1985, (In Russian.) 0617.46035 Google Scholar[15] L. V. Kantorovich and , G. P. Akilov, Functional Analysis, Pergamon Press, Oxford, New York, 1980 Google Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails BEncyclopaedia of Mathematics | 1 Jan 1997 Cross Ref Volume 35, Issue 3| 1991Theory of Probability & Its Applications History Submitted:21 December 1987Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1135069Article page range:pp. 500-512ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics