Saddlepoint Approximations With Applications

Author : Ronald W. Butler
Publisher : Cambridge University Press
Page : 548 pages
File Size : 40,5 Mb
Release : 2007-08-16
Category : Mathematics
ISBN : 9781139466516

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Saddlepoint Approximations with Applications by Ronald W. Butler Pdf

Modern statistical methods use complex, sophisticated models that can lead to intractable computations. Saddlepoint approximations can be the answer. Written from the user's point of view, this book explains in clear language how such approximate probability computations are made, taking readers from the very beginnings to current applications. The core material is presented in chapters 1-6 at an elementary mathematical level. Chapters 7-9 then give a highly readable account of higher-order asymptotic inference. Later chapters address areas where saddlepoint methods have had substantial impact: multivariate testing, stochastic systems and applied probability, bootstrap implementation in the transform domain, and Bayesian computation and inference. No previous background in the area is required. Data examples from real applications demonstrate the practical value of the methods. Ideal for graduate students and researchers in statistics, biostatistics, electrical engineering, econometrics, and applied mathematics, this is both an entry-level text and a valuable reference.

Author : Jens Ledet Jensen
Publisher : Oxford University Press
Page : 348 pages
File Size : 50,6 Mb
Release : 1995
Category : Mathematics
ISBN : 0198522959

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Saddlepoint Approximations by Jens Ledet Jensen Pdf

This book explains the ideas behind the saddlepoint approximations as well as giving a detailed mathematical description of the subject and many worked out examples.

Author : Yue Kuen Kwok,Wendong Zheng
Publisher : Springer
Page : 128 pages
File Size : 54,6 Mb
Release : 2018-02-16
Category : Mathematics
ISBN : 9783319741017

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Saddlepoint Approximation Methods in Financial Engineering by Yue Kuen Kwok,Wendong Zheng Pdf

This book summarizes recent advances in applying saddlepoint approximation methods to financial engineering. It addresses pricing exotic financial derivatives and calculating risk contributions to Value-at-Risk and Expected Shortfall in credit portfolios under various default correlation models. These standard problems involve the computation of tail probabilities and tail expectations of the corresponding underlying state variables. The text offers in a single source most of the saddlepoint approximation results in financial engineering, with different sets of ready-to-use approximation formulas. Much of this material may otherwise only be found in original research publications. The exposition and style are made rigorous by providing formal proofs of most of the results. Starting with a presentation of the derivation of a variety of saddlepoint approximation formulas in different contexts, this book will help new researchers to learn the fine technicalities of the topic. It will also be valuable to quantitative analysts in financial institutions who strive for effective valuation of prices of exotic financial derivatives and risk positions of portfolios of risky instruments.

Author : John E. Kolassa
Publisher : Springer Science & Business Media
Page : 162 pages
File Size : 55,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475742756

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Series Approximation Methods in Statistics by John E. Kolassa Pdf

This book was originally compiled for a course I taught at the University of Rochester in the fall of 1991, and is intended to give advanced graduate students in statistics an introduction to Edgeworth and saddlepoint approximations, and related techniques. Many other authors have also written monographs on this subject, and so this work is narrowly focused on two areas not recently discussed in theoretical text books. These areas are, first, a rigorous consideration of Edgeworth and saddlepoint expansion limit theorems, and second, a survey of the more recent developments in the field. In presenting expansion limit theorems I have drawn heavily 011 notation of McCullagh (1987) and on the theorems presented by Feller (1971) on Edgeworth expansions. For saddlepoint notation and results I relied most heavily on the many papers of Daniels, and a review paper by Reid (1988). Throughout this book I have tried to maintain consistent notation and to present theorems in such a way as to make a few theoretical results useful in as many contexts as possible. This was not only in order to present as many results with as few proofs as possible, but more importantly to show the interconnections between the various facets of asymptotic theory. Special attention is paid to regularity conditions. The reasons they are needed and the parts they play in the proofs are both highlighted.

Author : Philippe Flajolet,Robert Sedgewick
Publisher : Cambridge University Press
Page : 825 pages
File Size : 48,9 Mb
Release : 2009-01-15
Category : Mathematics
ISBN : 9781139477161

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Analytic Combinatorics by Philippe Flajolet,Robert Sedgewick Pdf

Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.

Author : Anirban DasGupta
Publisher : Springer Science & Business Media
Page : 726 pages
File Size : 55,9 Mb
Release : 2008-03-07
Category : Mathematics
ISBN : 9780387759708

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Asymptotic Theory of Statistics and Probability by Anirban DasGupta Pdf

This unique book delivers an encyclopedic treatment of classic as well as contemporary large sample theory, dealing with both statistical problems and probabilistic issues and tools. The book is unique in its detailed coverage of fundamental topics. It is written in an extremely lucid style, with an emphasis on the conceptual discussion of the importance of a problem and the impact and relevance of the theorems. There is no other book in large sample theory that matches this book in coverage, exercises and examples, bibliography, and lucid conceptual discussion of issues and theorems.

Author : Thomas Höglund
Publisher : Unknown
Page : 8 pages
File Size : 46,9 Mb
Release : 1978
Category : Electronic
ISBN : OCLC:7157452

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Saddle Point Approximations with Applications to the Central Limit Problem and Statistical Inference by Thomas Höglund Pdf

Author : Marc Moore,Constance van Eeden
Publisher : IMS
Page : 532 pages
File Size : 52,8 Mb
Release : 2003
Category : Mathematical statistics
ISBN : 0940600579

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Mathematical Statistics and Applications by Marc Moore,Constance van Eeden Pdf

Author : Rolf-Dieter Reiss
Publisher : Springer Science & Business Media
Page : 363 pages
File Size : 49,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461396208

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Approximate Distributions of Order Statistics by Rolf-Dieter Reiss Pdf

This book is designed as a unified and mathematically rigorous treatment of some recent developments of the asymptotic distribution theory of order statistics (including the extreme order statistics) that are relevant for statistical theory and its applications. Particular emphasis is placed on results concern ing the accuracy oflimit theorems, on higher order approximations, and other approximations in quite a general sense. Contrary to the classical limit theorems that primarily concern the weak convergence of distribution functions, our main results will be formulated in terms of the variational and the Hellinger distance. These results will form the proper springboard for the investigation of parametric approximations of nonparametric models of joint distributions of order statistics. The approxi mating models include normal as well as extreme value models. Several applications will show the usefulness of this approach. Other recent developments in statistics like nonparametric curve estima tion and the bootstrap method will be studied as far as order statistics are concerned. 1n connection with this, graphical methods will, to some extent, be explored.

Author : Anonim
Publisher : John Wiley & Sons
Page : 722 pages
File Size : 48,7 Mb
Release : 2005-12-16
Category : Mathematics
ISBN : 9780471743910

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Encyclopedia of Statistical Sciences, Volume 1 by Anonim Pdf

ENCYCLOPEDIA OF STATISTICAL SCIENCES

Author : Ying-ming Jou
Publisher : Unknown
Page : 144 pages
File Size : 54,8 Mb
Release : 1997
Category : Electronic
ISBN : CORNELL:31924080031846

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Application of the Saddlepoint Approximation to Estimating the Variance of a Function by Ying-ming Jou Pdf

Author : Andreas Makrides,Alex Karagrigoriou,Christos H. Skiadas
Publisher : John Wiley & Sons
Page : 241 pages
File Size : 43,9 Mb
Release : 2020-04-09
Category : Mathematics
ISBN : 9781119721581

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Data Analysis and Applications 4 by Andreas Makrides,Alex Karagrigoriou,Christos H. Skiadas Pdf

Data analysis as an area of importance has grown exponentially, especially during the past couple of decades. This can be attributed to a rapidly growing computer industry and the wide applicability of computational techniques, in conjunction with new advances of analytic tools. This being the case, the need for literature that addresses this is self-evident. New publications are appearing, covering the need for information from all fields of science and engineering, thanks to the universal relevance of data analysis and statistics packages. This book is a collective work by a number of leading scientists, analysts, engineers, mathematicians and statisticians who have been working at the forefront of data analysis. The chapters included in this volume represent a cross-section of current concerns and research interests in these scientific areas. The material is divided into three parts: Financial Data Analysis and Methods, Statistics and Stochastic Data Analysis and Methods, and Demographic Methods and Data Analysis- providing the reader with both theoretical and applied information on data analysis methods, models and techniques and appropriate applications.

Author : Samuel Kotz,Norman L. Johnson
Publisher : Springer Science & Business Media
Page : 576 pages
File Size : 55,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461206675

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Breakthroughs in Statistics by Samuel Kotz,Norman L. Johnson Pdf

Volume III includes more selections of articles that have initiated fundamental changes in statistical methodology. It contains articles published before 1980 that were overlooked in the previous two volumes plus articles from the 1980's - all of them chosen after consulting many of today's leading statisticians.

Author : Manfred Opper,David Saad
Publisher : MIT Press
Page : 300 pages
File Size : 40,6 Mb
Release : 2001
Category : Computers
ISBN : 0262150549

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Advanced Mean Field Methods by Manfred Opper,David Saad Pdf

This book covers the theoretical foundations of advanced mean field methods, explores the relation between the different approaches, examines the quality of the approximation obtained, and demonstrates their application to various areas of probabilistic modeling. A major problem in modern probabilistic modeling is the huge computational complexity involved in typical calculations with multivariate probability distributions when the number of random variables is large. Because exact computations are infeasible in such cases and Monte Carlo sampling techniques may reach their limits, there is a need for methods that allow for efficient approximate computations. One of the simplest approximations is based on the mean field method, which has a long history in statistical physics. The method is widely used, particularly in the growing field of graphical models. Researchers from disciplines such as statistical physics, computer science, and mathematical statistics are studying ways to improve this and related methods and are exploring novel application areas. Leading approaches include the variational approach, which goes beyond factorizable distributions to achieve systematic improvements; the TAP (Thouless-Anderson-Palmer) approach, which incorporates correlations by including effective reaction terms in the mean field theory; and the more general methods of graphical models. Bringing together ideas and techniques from these diverse disciplines, this book covers the theoretical foundations of advanced mean field methods, explores the relation between the different approaches, examines the quality of the approximation obtained, and demonstrates their application to various areas of probabilistic modeling.

Author : Pamela Ann Ohman
Publisher : Unknown
Page : 218 pages
File Size : 41,8 Mb
Release : 1997
Category : Electronic
ISBN : CORNELL:31924080068327

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Approximated and Estimated Saddlepoint Approximations by Pamela Ann Ohman Pdf