Berkeley Symposium Research Articles

The Complex Normal Distribution and Admissibility of the Sample Average as an Estimate of a Location Parameter

Previous article Next article The Complex Normal Distribution and Admissibility of the Sample Average as an Estimate of a Location ParameterA. L. RukhinA. L. Rukhinhttps://doi.org/10.1137/1112087PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] A. M. Kagan, , Yu. V. Linnik and , C. Radhakrishna Rao, On a characterization of the normal law based on a property of the sample average, Sankhyā Ser. A, 27 (1965), 405–406 MR0200999 0168.40203 Google Scholar[2] Charles Stein, Inadmissibility of the usual estimator for the mean of a multivariate normal distribution, Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1954–1955, vol. I, University of California Press, Berkeley and Los Angeles, 1956, 197–206 MR0084922 0073.35602 Google Scholar[3] J. L. Hodges, Jr. and , E. L. Lehmann, Some applications of the Cramér-Rao inequality, Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability, 1950, University of California Press, Berkeley and Los Angeles, 1951, 13–22 MR0044795 0044.14404 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Volume 12, Issue 4| 1967Theory of Probability & Its Applications History Submitted:03 November 1966Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1112087Article page range:pp. 695-697ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics

Fifth Berkeley Symposium on Statistics and Probability

Fifth Berkeley Symposium on Statistics and Probability

Fifth Berkeley Symposium on Statistics and Probability

Fifth Berkeley Symposium on Statistics and Probability

Non-Linear Programming with Randomization

This paper considers non-linear programming models in which randomized solutions are allowed. That is, we consider the minimization of the expected value of a non-linear function subject to constraints on the expectation of nonlinear functions, where the expectations are taken with respect to randomized decision strategies. Saddle-point and related optimality conditions similar to those given in [Karlin, S. 1959. Mathematical Methods and Theory in Games, Programming, and Economics, Vol. 1, Chapter 7, Addison-Wesley.] and [Kuhn, H. W., A. W. Tucker. 1951. Nonlinear programming. Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability. University of California Press, 481–492.] for convex functions are obtained with only very mild restrictions on the shape of the optimizing and constraint functions. We also consider when the optimal solution need not be randomized and how the notions of Lagrange multipliers and game theory are related to our results. We offer an economic interpretation of our solution. A few simple examples are given to illustrate the implications of randomized strategies. It is also pointed out how the results of this paper are related to the decomposition methods widely used to solve mathematical programming problems.

Some Properties of Estimators of the Spectrum of a Stationary Process

Previous article Next article Some Properties of Estimators of the Spectrum of a Stationary ProcessT. L. MalevichT. L. Malevichhttps://doi.org/10.1137/1110053PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] I. A. Ibragimov, On estimation of the spectral function of a stationary Gaussian process, Theory Prob. Applications, 8 (1963), 366–401, (English translation.) 10.1137/1108044 0137.12901 LinkGoogle Scholar[2] I. A. Ibragimov, Estimate of the spectrum of a stationary Gaussian process, Dokl. Akad. Nauk SSSR, 141 (1961), 296–299, (In Russian.) MR0131950 Google Scholar[3] Ulf Grenander and , Murray Rosenblatt, Statistical analysis of stationary time series, John Wiley & Sons, New York, 1957, 300– MR0084975 0080.12904 Google Scholar[4] Ulf Grenander and , Murray Rosenblatt, Some problems in estimating the spectrum of a time series, Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, 1954–1955, vol. I, University of California Press, Berkeley and Los Angeles, 1956, 77–93 MR0084914 0072.36401 Google Scholar[5] T. L. Malevich, The asymptotic behavior of an estimate for the spectral function of a stationary Gaussian process, Theory Prob. Applications, 9 (1964), 350–353, (English translation.) 10.1137/1109052 0132.38401 LinkGoogle Scholar[6] I. A. Ibragimov and , T. M. Tovstik, An estimate for spectral functions of a class of stationary random sequences, Vestnik Leningrad. Univ. Ser. Mat. Meh. Astronom., 19 (1964), 42–57, (In Russian.) MR0165585 Google Scholar[7] S. N. Bernshtein, Probability Theory, Gostekhizdat, Moskva, 1946, (In Russian.) Google Scholar[9] G. M. Fikhtengol'ts, Course on Differential and Integral Calculus, Vol. III, Gostekhizdat, Moskva, 1949, (In Russian.) Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Asymptotic properties of spectral estimates of second order9 November 2011 Cross Ref On the Uniform Convergence of Estimates of the Spectral Density of a Stationary Gaussian Random ProcessV. G. Alekseev28 July 2006 | Theory of Probability & Its Applications, Vol. 19, No. 1AbstractPDF (608 KB)Asymptotic Normality of the Number of Crossings of Level Zero by a Gaussian ProcessT. L. Malevich17 July 2006 | Theory of Probability & Its Applications, Vol. 14, No. 2AbstractPDF (630 KB) Volume 10, Issue 3| 1965Theory of Probability & Its Applications History Submitted:14 April 1964Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1110053Article page range:pp. 457-465ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics

Asymptotic Efficiency of the Maximum Likelihood Estimator

Asymptotic Efficiency of the Maximum Likelihood Estimator

Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability: Volume II, Contributions to Probability Theory.

Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability: Volume II, Contributions to Probability Theory.

Boekbesprekingen

Book reviewed in this article:Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability Vol. 1: Contributions to the Theory of Statistics; Ed. J. NEYMANThe method of paired comparisons, H. A. DAVIDBasic Concepts of Probability and Statistics, J. L. HODGES Jr. and E. L. LEHMANNStatistical mapping and the presentation of statistics, G. C. DICKINSONStudies in mathematical analysis and related topics, essays in honor of George Polya, edited by GABOR SZEGÓ, CHARLES LOEWNER, STEFAN BERGMAN, MENAHEM MAX SCHIFFER, JERZY NEYMAN, DAVID GILBURG and HERBERT SOLOMON

Reviews

Book reviewed in this article:Papers on Human Genetics. Edited by Samuel H. Boyer, IV. Englewood Cliffs, N. J.: Prentice‐Hall Inc. and London: Prentice‐Hall International. 1964. Methodology in Basic Genetics. Edited by Walter J. Burdette. Holden‐Day, Inc. 1963. The Process of Evolution. Edited by P. R. Ehrlich and R. W. Holm. New York, San Francisco, Toronto and London: McGraw‐Hill. 1963. Teaching Genetics. Edited by C. D. Darlington and A. D. Bradshaw. Edinburgh: Oliver and Boyd Ltd. 1963. Principles of Numerical Taxonomy. By R. R. Sokal and P. H. A. Sneath. San Francisco and London: W. H. Freeman and Company. 1963. General Physiology of Cell Specialization. Edited by Daniel Mazia and Albert Tyler. 1963. New York, McGraw‐Hill Die angeborenen Stoffwechselanomalien. Grundlagen. Klinik. Therapie. By K. Schreier, in collaboration with H. Mattern, U. Porath and J. Spranger, and with a contribution by H.‐G. Lasch. Stuttgart: Georg Thieme. 1963. Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability, vol. iv, Biology and Problems of Health. Edited By Jerzy Neyman. Berkeley and Los Angeles: University of California Press. 161.

Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability. Vol. IV: Biology and Problems of Health. Edited by Jerzy Neyman, University of California Press, Berkeley and Los Angeles, 1961. X + 413 S. Preis $ 8,80

Biometrische ZeitschriftVolume 6, Issue 4 p. 279-279 Buchbesprechung Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability. Vol. IV: Biology and Problems of Health. Edited by Jerzy Neyman, University of California Press, Berkeley and Los Angeles, 1961. X + 413 S. Preis $ 8,80 E. Weber, E. WeberSearch for more papers by this author E. Weber, E. WeberSearch for more papers by this author First published: 1964 https://doi.org/10.1002/bimj.19640060422AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume6, Issue41964Pages 279-279 RelatedInformation

Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability. Volume IV: Contributions to Biology and Problems of Medicine. Held at the Statistical Laboratory.Jerzy Neyman

<i>Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability. Volume IV: Contributions to Biology and Problems of Medicine. Held at the Statistical Laboratory.</i>Jerzy Neyman

Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability. Volume IV: Biology and Problems of Health.

Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability. Volume IV: Biology and Problems of Health.

Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability.

Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability.

Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability. Volume IV: Biology and Problems of Health.

Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability. Volume IV: Biology and Problems of Health.

Book Reviews

Book Reviews

Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability. Vol. I. Theory of Statistics.

Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability. Vol. I. Theory of Statistics.

Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability. Vol. III: Contributions to Astronomy, Meteorology and Physics

Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability. Vol. III: Contributions to Astronomy, Meteorology and Physics

Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability. Volume IV

Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability. Volume IV

Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability. Volume IV. Contributions to Biology and Problems of Medicine

Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability. Volume IV. Contributions to Biology and Problems of Medicine

Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability. Volume II: Probability Theory (J. Neyman ed.)

Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability. Volume II: Probability Theory (J. Neyman ed.)