Saddlepoint Approximations

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Saddlepoint Approximations With Applications

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Author : Ronald W. Butler
language : en
Publisher: Cambridge University Press
Release Date : 2007-08-16

Saddlepoint Approximations With Applications written by Ronald W. Butler and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-08-16 with Mathematics categories.

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.

Saddlepoint Approximations

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Author : Jens Ledet Jensen
language : en
Publisher: Oxford University Press
Release Date : 1995

Saddlepoint Approximations written by Jens Ledet Jensen and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.

Although introduced more than 60 years ago it is only during the last 15 years that there has been a systematic development of saddlepoint approximations. These approximations give a highly accurate expression for the tail of a distribution, not only in the centre of the distribution but also for very small tail probabilities. The price for this is a more cumbersome formula, the evaluation of which sometimes requires the use of a small personal computer. This book explains the ideas behind the saddlepoint approximations as well as giving a detailed mathematical description of the subject. The emphasis is two- fold. One is on popularizing the formulae through many worked out and ready to use examples. The second is on giving a comprehensive mathematical background for further research in the field. Some of the major subjects treated are uniformity of the approximations, tests in exponential families, and compound sums with applications in insurance mathematics.

Saddlepoint Approximation Methods In Financial Engineering

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Author : Yue Kuen Kwok
language : en
Publisher: Springer
Release Date : 2018-02-16

Saddlepoint Approximation Methods In Financial Engineering written by Yue Kuen Kwok and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-16 with Mathematics categories.

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.

Series Approximation Methods In Statistics

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Author : John E. Kolassa
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Series Approximation Methods In Statistics written by John E. Kolassa and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.

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.

Elements Of Distribution Theory

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Author : Thomas A. Severini
language : en
Publisher: Cambridge University Press
Release Date : 2005-08-08

Elements Of Distribution Theory written by Thomas A. Severini and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-08 with Mathematics categories.

This detailed introduction to distribution theory uses no measure theory, making it suitable for students in statistics and econometrics as well as for researchers who use statistical methods. Good backgrounds in calculus and linear algebra are important and a course in elementary mathematical analysis is useful, but not required. An appendix gives a detailed summary of the mathematical definitions and results that are used in the book. Topics covered range from the basic distribution and density functions, expectation, conditioning, characteristic functions, cumulants, convergence in distribution and the central limit theorem to more advanced concepts such as exchangeability, models with a group structure, asymptotic approximations to integrals, orthogonal polynomials and saddlepoint approximations. The emphasis is on topics useful in understanding statistical methodology; thus, parametric statistical models and the distribution theory associated with the normal distribution are covered comprehensively.

Approximated And Estimated Saddlepoint Approximations

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Author : Pamela Ann Ohman
language : en
Publisher:
Release Date : 1997

Approximated And Estimated Saddlepoint Approximations written by Pamela Ann Ohman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with categories.

Saddlepoint Approximations Edgeworth Expansions And Normal Approximations

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Author : Jens Ledet Jensen
language : en
Publisher:
Release Date : 1993

Saddlepoint Approximations Edgeworth Expansions And Normal Approximations written by Jens Ledet Jensen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Approximation theory categories.

Directional And Multivariate Statistics

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Author : Somesh Kumar
language : en
Publisher: Springer Nature
Release Date : 2025-05-05

Directional And Multivariate Statistics written by Somesh Kumar and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-05 with Mathematics categories.

This book contains select chapters on a range of topics in directional statistics, multivariate statistical inference, financial statistics, statistical machine learning and reliability inference. At the 43rd Annual Convention of the Indian Society for Probability and Statistics (ISPS) held in Prayagraj (formerly Allahabad), Uttar Pradesh, India, from 6–8 February 2024, attribute was paid to Prof. Ashis SenGupta on the occasion of his 70th birthday. He has pioneered research on directional statistics in the modern era in India and enhanced it worldwide and contributed significantly to the advancement of the following topics: Highly flexible distributions on manifolds Statistical machine learning in data science Big data on manifolds Optimal multiparameter, multivariate statistical inference Reliability inference and stress-dependent-strength models Directional statistics for highly volatile financial models Cylindrical, spherical and toroidal regression analysis Innovative applications of emerging real-life directional data

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Author :
language : en
Publisher: World Scientific
Release Date :

written by and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Crossing Boundaries

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Author : John Edward Kolassa
language : en
Publisher: IMS
Release Date : 2003

Crossing Boundaries written by John Edward Kolassa and has been published by IMS this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.