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Inequalities And Extremal Problems In Probability And Statistics

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Inequalities and Extremal Problems in Probability and Statistics

Inequalities and Extremal Problems in Probability and Statistics Book
Author : Iosif Pinelis,Victor H. de la Peña,Rustam Ibragimov,Adam Osȩkowski,Irina Shevtsova
Publisher : Academic Press
Release : 2017-05-10
ISBN : 0128098929
Language : En, Es, Fr & De

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Book Description :

Inequalities and Extremal Problems in Probability and Statistics: Selected Topics presents various kinds of useful inequalities that are applicable in many areas of mathematics, the sciences, and engineering. The book enables the reader to grasp the importance of inequalities and how they relate to probability and statistics. This will be an extremely useful book for researchers and graduate students in probability, statistics, and econometrics, as well as specialists working across sciences, engineering, financial mathematics, insurance, and mathematical modeling of large risks. Teaches users how to understand useful inequalities Applicable across mathematics, sciences, and engineering Presented by a team of leading experts

Some Topics in Probability Theory Combinatorics and Information Theory

Some Topics in Probability Theory  Combinatorics and Information Theory Book
Author : Jiange Li
Publisher : Unknown
Release : 2016
ISBN : 9781369128710
Language : En, Es, Fr & De

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Book Description :

This dissertation explores three topics at the intersection of probability theory, combinatorics and information theory. The first part focuses on studying small ball inequalities for sums and differences of independent, identically distributed random variables taking values in very general sets. Depending on the setting (abelian or non-abelian groups, or vector spaces, or Banach spaces) we provide a collection of inequalities relating different small ball probabilities that are sharp in many cases of interest. We show that underlying these distribution-free probabilistic inequalities are inequalities of extremal combinatorial nature, related among other things to classical packing problems such as the kissing number problem. As regards applications, we develop various moment inequalities. The second part is devoted to exploring a formal parallel relation between entropy inequalities in information theory and sumset estimates in additive combinatorics. Our work is closely related to the study of more-sum-than-difference sets in additive combinatorics. Various information theoretical inequalities are obtained, such as the entropy analogue of Freiman-Pigarev inequality. We also present applications of our results in the construction of polar codes with significantly improved error probability compared to the canonical construction. Concentration of measure principle is one of the cornerstones in geometric functional analysis and probability theory, and it is widely used in many other areas. In the third part, we study the concentration property of information content, which is one of the central interests in information theory, and it has great relevance with various other areas such as probability theory, statistics and statistical physics. Sharp exponential deviation estimates for the information content as well as a sharp bound on the varentropy for convex probability measures are obtained on Euclidean spaces.

Mathematical Reviews

Mathematical Reviews Book
Author : Anonim
Publisher : Unknown
Release : 2001
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Mathematical Reviews book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Analysis of Step Stress Models

Analysis of Step Stress Models Book
Author : Debasis Kundu,Ayon Ganguly
Publisher : Academic Press
Release : 2017-06-29
ISBN : 0081012403
Language : En, Es, Fr & De

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Book Description :

Analysis of Step-Stress Models: Existing Results and Some Recent Developments describes, in detail, the step-stress models and related topics that have received significant attention in the last few years. Although two books, Bagdonavicius and Nikulin (2001) and Nelson (1990), on general accelerated life testing models are available, no specific book is available on step-stress models. Due to the importance of this particular topic, Balakrishnan (2009) provided an excellent review for exponential step-stress models. The scope of this book is much more, providing the inferential issues for different probability models, both from the frequentist and Bayesian points-of-view. Explains the different distributions of the Cumulative Exposure Mode Covers many different models used for step-stress analysis Discusses Step-stress life testing under the competing or complementary risk model

Notices of the American Mathematical Society

Notices of the American Mathematical Society Book
Author : American Mathematical Society
Publisher : Unknown
Release : 1988
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Notices of the American Mathematical Society book written by American Mathematical Society, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Lectures on Advances in Combinatorics

Lectures on Advances in Combinatorics Book
Author : Rudolf Ahlswede,Vladimir Blinovsky
Publisher : Springer Science & Business Media
Release : 2008-05-17
ISBN : 9783540786023
Language : En, Es, Fr & De

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Book Description :

The lectures concentrate on highlights in Combinatorial (ChaptersII and III) and Number Theoretical (ChapterIV) Extremal Theory, in particular on the solution of famous problems which were open for many decades. However, the organization of the lectures in six chapters does neither follow the historic developments nor the connections between ideas in several cases. With the speci?ed auxiliary results in ChapterI on Probability Theory, Graph Theory, etc., all chapters can be read and taught independently of one another. In addition to the 16 lectures organized in 6 chapters of the main part of the book, there is supplementary material for most of them in the Appendix. In parti- lar, there are applications and further exercises, research problems, conjectures, and even research programs. The following books and reports [B97], [ACDKPSWZ00], [A01], and [ABCABDM06], mostly of the authors, are frequently cited in this book, especially in the Appendix, and we therefore mark them by short labels as [B], [N], [E], and [G]. We emphasize that there are also “Exercises” in [B], a “Problem Section” with contributions by several authors on pages 1063–1105 of [G], which are often of a combinatorial nature, and “Problems and Conjectures” on pages 172–173 of [E].

Contributions to Probability and Statistics

Contributions to Probability and Statistics Book
Author : Leon J. Gleser,Michael D. Perlman,S. James Press,Allan R. Sampson
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 1461236789
Language : En, Es, Fr & De

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Book Description :

Published in honor of the sixty-fifth birthday of Professor Ingram Olkin of Stanford University. Part I contains a brief biography of Professor Olkin and an interview with him discussing his career and his research interests. Part II contains 32 technical papers written in Professor Olkin's honor by his collaborators, colleagues, and Ph.D. students. These original papers cover a wealth of topics in mathematical and applied statistics, including probability inequalities and characterizations, multivariate analysis and association, linear and nonlinear models, ranking and selection, experimental design, and approaches to statistical inference. The volume reflects the wide range of Professor Olkin's interests in and contributions to research in statistics, and provides an overview of new developments in these areas of research.

Tchebycheff Systems

Tchebycheff Systems Book
Author : Samuel Karlin,William J. Studden
Publisher : Unknown
Release : 1966
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

This research monograph presents information on an important tool for mathematical analysis in such areas as the theory of approximations, boundary value problems, and the theory of inequaklities. Approximately one third of the results given are new, and almost all the material, including background discussions, is set forth in a unified manner, with stress on the geometric approach.

High Dimensional Probability

High Dimensional Probability Book
Author : Ernst Eberlein,Marjorie Hahn
Publisher : Birkhäuser
Release : 2012-12-06
ISBN : 3034888295
Language : En, Es, Fr & De

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Book Description :

What is high dimensional probability? Under this broad name we collect topics with a common philosophy, where the idea of high dimension plays a key role, either in the problem or in the methods by which it is approached. Let us give a specific example that can be immediately understood, that of Gaussian processes. Roughly speaking, before 1970, the Gaussian processes that were studied were indexed by a subset of Euclidean space, mostly with dimension at most three. Assuming some regularity on the covariance, one tried to take advantage of the structure of the index set. Around 1970 it was understood, in particular by Dudley, Feldman, Gross, and Segal that a more abstract and intrinsic point of view was much more fruitful. The index set was no longer considered as a subset of Euclidean space, but simply as a metric space with the metric canonically induced by the process. This shift in perspective subsequently lead to a considerable clarification of many aspects of Gaussian process theory, and also to its applications in other settings.

Decoupling

Decoupling Book
Author : Victor de la Peña,Evarist Giné
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 1461205379
Language : En, Es, Fr & De

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Book Description :

A friendly and systematic introduction to the theory and applications. The book begins with the sums of independent random variables and vectors, with maximal inequalities and sharp estimates on moments, which are later used to develop and interpret decoupling inequalities. Decoupling is first introduced as it applies to randomly stopped processes and unbiased estimation. The authors then proceed with the theory of decoupling in full generality, paying special attention to comparison and interplay between martingale and decoupling theory, and to applications. These include limit theorems, moment and exponential inequalities for martingales and more general dependence structures, biostatistical implications, and moment convergence in Anscombe's theorem and Wald's equation for U--statistics. Addressed to researchers in probability and statistics and to graduates, the expositon is at the level of a second graduate probability course, with a good portion of the material fit for use in a first year course.

Journal of the American Statistical Association

Journal of the American Statistical Association Book
Author : American Statistical Association
Publisher : Unknown
Release : 1996
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Journal of the American Statistical Association book written by American Statistical Association, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Inequalities Involving Functions and Their Integrals and Derivatives

Inequalities Involving Functions and Their Integrals and Derivatives Book
Author : Dragoslav S. Mitrinovic,J. Pecaric,A.M Fink
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 9401135622
Language : En, Es, Fr & De

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Book Description :

One service mathematics has rendered the ~l moil ..., Ii j'avait su comment en revenir, je n'y serais point aUe.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'(ftre of this series.

Comprehensive Dissertation Index 1861 1972 Mathematics and statistics

Comprehensive Dissertation Index  1861 1972  Mathematics and statistics Book
Author : Xerox University Microfilms
Publisher : Unknown
Release : 1973
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Comprehensive Dissertation Index 1861 1972 Mathematics and statistics book written by Xerox University Microfilms, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Moments in Mathematics

Moments in Mathematics Book
Author : Henry J. Landau
Publisher : American Mathematical Soc.
Release : 1987
ISBN : 9780821801147
Language : En, Es, Fr & De

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Book Description :

Function theory, spectral decomposition of operators, probability, approximation, electrical and mechanical inverse problems, prediction of stochastic processes, the design of algorithms for signal-processing VLSI chips--these are among a host of important theoretical and applied topics illuminated by the classical moment problem. To survey some of these ramifications and the research which derives from them, the AMS sponsored the Short Course Moments in Mathematics at the Joint Mathematics Meetings, held in San Antonio, Texas, in January 1987. This volume contains the six lectures presented during that course. The papers are likely to find a wide audience, for they are expository, but nevertheless lead the reader to topics of current research. In his paper, Henry J. Landau sketches the main ideas of past work related to the moment problem by such mathematicians as Caratheodory, Herglotz, Schur, Riesz, and Krein and describes the way the moment problem has interconnected so many diverse areas of research. J. H. B. Kemperman examines the moment problem from a geometric viewpoint which involves a certain natural duality method and leads to interesting applications in linear programming, measure theory, and dilations. Donald Sarason first provides a brief review of the theory of unbounded self-adjoint operators then goes on to sketch the operator-theoretic treatment of the Hamburger problem and to discuss Hankel operators, the Adamjan-Arov-Krein approach, and the theory of unitary dilations. Exploring the interplay of trigonometric moment problems and signal processing, Thomas Kailath describes the role of Szego polynomials in linear predictive coding methods, parallel implementation, one-dimensional inverse scattering problems, and the Toeplitz moment matrices. Christian Berg contrasts the multi-dimensional moment problem with the one-dimensional theory and shows how the theory of the moment problem may be viewed as part of harmonic analysis on semigroups. Starting from a historical survey of the use of moments in probability and statistics, Persi Diaconis illustrates the continuing vitality of these methods in a variety of recent novel problems drawn from such areas as Wiener-Ito integrals, random graphs and matrices, Gibbs ensembles, cumulants and self-similar processes, projections of high-dimensional data, and empirical estimation.

The Theory of Canonical Moments with Applications in Statistics Probability and Analysis

The Theory of Canonical Moments with Applications in Statistics  Probability  and Analysis Book
Author : Holger Dette,William J. Studden
Publisher : John Wiley & Sons
Release : 1997-09-08
ISBN : 9780471109914
Language : En, Es, Fr & De

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Book Description :

This new material is concerned with the theory and applications of probability, statistics and analysis of canonical moments. It provides a powerful tool for the determination of optimal experimental designs, for the calculation of the main characteristics of random walks, and for other moment problems appearing in probability and statistics.

Concentration Inequalities

Concentration Inequalities Book
Author : Stéphane Boucheron,Gábor Lugosi,Pascal Massart
Publisher : OUP Oxford
Release : 2013-02-08
ISBN : 0191655503
Language : En, Es, Fr & De

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Book Description :

Concentration inequalities for functions of independent random variables is an area of probability theory that has witnessed a great revolution in the last few decades, and has applications in a wide variety of areas such as machine learning, statistics, discrete mathematics, and high-dimensional geometry. Roughly speaking, if a function of many independent random variables does not depend too much on any of the variables then it is concentrated in the sense that with high probability, it is close to its expected value. This book offers a host of inequalities to illustrate this rich theory in an accessible way by covering the key developments and applications in the field. The authors describe the interplay between the probabilistic structure (independence) and a variety of tools ranging from functional inequalities to transportation arguments to information theory. Applications to the study of empirical processes, random projections, random matrix theory, and threshold phenomena are also presented. A self-contained introduction to concentration inequalities, it includes a survey of concentration of sums of independent random variables, variance bounds, the entropy method, and the transportation method. Deep connections with isoperimetric problems are revealed whilst special attention is paid to applications to the supremum of empirical processes. Written by leading experts in the field and containing extensive exercise sections this book will be an invaluable resource for researchers and graduate students in mathematics, theoretical computer science, and engineering.

Journal of Research of the National Bureau of Standards

Journal of Research of the National Bureau of Standards Book
Author : Anonim
Publisher : Unknown
Release : 1961
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Journal of Research of the National Bureau of Standards book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Current Index to Statistics Applications Methods and Theory

Current Index to Statistics  Applications  Methods and Theory Book
Author : Anonim
Publisher : Unknown
Release : 1999
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Current Index to Statistics Applications Methods and Theory book written by , available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Banach Spaces and their Applications in Analysis

Banach Spaces and their Applications in Analysis Book
Author : Beata Randrianantoanina,Narcisse Randrianantoanina
Publisher : Walter de Gruyter
Release : 2007-01-01
ISBN : 3110918293
Language : En, Es, Fr & De

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Book Description :

This volume contains contributions of principal speakers of a conference on Banach Spaces and their applications in analysis, held in May 2006 at Miami, Ohio, in honor of Nigel Kalton's 60th birthday. Its merit lies in the fact that it aims to encompass applications of Banach space methods in different areas of analysis, emphasizing versatility of the methods and underlying connections between seemingly distant areas of analysis.

High Dimensional Probability II

High Dimensional Probability II Book
Author : Evarist Giné,David M. Mason,Jon A. Wellner
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 1461213584
Language : En, Es, Fr & De

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Book Description :

High dimensional probability, in the sense that encompasses the topics rep resented in this volume, began about thirty years ago with research in two related areas: limit theorems for sums of independent Banach space valued random vectors and general Gaussian processes. An important feature in these past research studies has been the fact that they highlighted the es sential probabilistic nature of the problems considered. In part, this was because, by working on a general Banach space, one had to discard the extra, and often extraneous, structure imposed by random variables taking values in a Euclidean space, or by processes being indexed by sets in R or Rd. Doing this led to striking advances, particularly in Gaussian process theory. It also led to the creation or introduction of powerful new tools, such as randomization, decoupling, moment and exponential inequalities, chaining, isoperimetry and concentration of measure, which apply to areas well beyond those for which they were created. The general theory of em pirical processes, with its vast applications in statistics, the study of local times of Markov processes, certain problems in harmonic analysis, and the general theory of stochastic processes are just several of the broad areas in which Gaussian process techniques and techniques from probability in Banach spaces have made a substantial impact. Parallel to this work on probability in Banach spaces, classical proba bility and empirical process theory were enriched by the development of powerful results in strong approximations.