Inequalities and Extremal Problems in Probability and Statistics

• Author : Iosif Pinelis,Victor H. de la Peña,Rustam Ibragimov,Adam Osȩkowski,Irina Shevtsova
• Publisher : Academic Press
• Release : 10 May 2017

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

• Author : Debasis Kundu,Ayon Ganguly
• Publisher : Academic Press
• Release : 29 June 2017

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

• Author : Leon J. Gleser,Michael D. Perlman,S. James Press,Allan R. Sampson
• Publisher : Springer Science & Business Media
• Release : 06 December 2012

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

• Author : Victor de la Peña,Evarist Giné
• Publisher : Springer Science & Business Media
• Release : 06 December 2012

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

• Author : Ernst Eberlein,Marjorie Hahn
• Publisher : Birkhäuser
• Release : 06 December 2012

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

• Author : Dragoslav S. Mitrinovic,J. Pecaric,A.M Fink
• Publisher : Springer Science & Business Media
• Release : 06 December 2012

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

• Author : Stéphane Boucheron,Gábor Lugosi,Pascal Massart
• Publisher : OUP Oxford
• Release : 08 February 2013

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

• Author : Evarist Giné,David M. Mason,Jon A. Wellner
• Publisher : Springer Science & Business Media
• Release : 06 December 2012

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

• Author : Beata Randrianantoanina,Narcisse Randrianantoanina
• Publisher : Walter de Gruyter
• Release : 01 January 2007

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.

• Author : Luca Oneto
• Publisher : Springer
• Release : 17 July 2019

How can we select the best performing data-driven model? How can we rigorously estimate its generalization error? Statistical learning theory answers these questions by deriving non-asymptotic bounds on the generalization error of a model or, in other words, by upper bounding the true error of the learned model based just on quantities computed on the available data. However, for a long time, Statistical learning theory has been considered only an abstract theoretical framework, useful for inspiring new learning approaches, but

• Author : United States. National Bureau of Standards
• Publisher : Unknown
• Release : 23 March 1961

• Author : Henry J. Landau
• Publisher : American Mathematical Soc.
• Release : 23 March 1987

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

• Author : Christian Houdré,David M. Mason,Jan Rosiński,Jon A. Wellner
• Publisher : Springer Science & Business Media
• Release : 19 April 2013

This is a collection of papers by participants at High Dimensional Probability VI Meeting held from October 9-14, 2011 at the Banff International Research Station in Banff, Alberta, Canada. High Dimensional Probability (HDP) is an area of mathematics that includes the study of probability distributions and limit theorems in infinite-dimensional spaces such as Hilbert spaces and Banach spaces. The most remarkable feature of this area is that it has resulted in the creation of powerful new tools and perspectives, whose range

• Author : Moshe Shaked
• Publisher : IMS
• Release : 23 March 1992

• Author : Holger Dette,William J. Studden
• Publisher : John Wiley & Sons
• Release : 08 September 1997

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.