Approximated And Estimated Saddlepoint Approximations

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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

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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 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.

Application Of The Saddlepoint Approximation To Estimating The Variance Of A Function

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Author : Ying-ming Jou
language : en
Publisher:
Release Date : 1997

Application Of The Saddlepoint Approximation To Estimating The Variance Of A Function written by Ying-ming Jou 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 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.

Mathematical Statistics And Applications

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Author : Constance van Eeden
language : en
Publisher: IMS
Release Date : 2003

Mathematical Statistics And Applications written by Constance van Eeden 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.

Methods For Estimation And Inference In Modern Econometrics

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Author : Stanislav Anatolyev
language : en
Publisher: CRC Press
Release Date : 2011-06-07

Methods For Estimation And Inference In Modern Econometrics written by Stanislav Anatolyev and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-07 with Business & Economics categories.

This book covers important topics in econometrics. It discusses methods for efficient estimation in models defined by unconditional and conditional moment restrictions, inference in misspecified models, generalized empirical likelihood estimators, and alternative asymptotic approximations. The first chapter provides a general overview of established nonparametric and parametric approaches to estimation and conventional frameworks for statistical inference. The next several chapters focus on the estimation of models based on moment restrictions implied by economic theory. The final chapters cover nonconventional asymptotic tools that lead to improved finite-sample inference.

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.

Asymptotic Theory Of Statistics And Probability

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Author : Anirban DasGupta
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-03-07

Asymptotic Theory Of Statistics And Probability written by Anirban DasGupta 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 2008-03-07 with Mathematics categories.

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.

Stochastic Approximation And Recursive Algorithms And Applications

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Author : Harold Kushner
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-04

Stochastic Approximation And Recursive Algorithms And Applications written by Harold Kushner 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 2006-05-04 with Mathematics categories.

The basic stochastic approximation algorithms introduced by Robbins and MonroandbyKieferandWolfowitzintheearly1950shavebeenthesubject of an enormous literature, both theoretical and applied. This is due to the large number of applications and the interesting theoretical issues in the analysis of “dynamically de?ned” stochastic processes. The basic paradigm is a stochastic di?erence equation such as ? = ? + Y , where ? takes n+1 n n n n its values in some Euclidean space, Y is a random variable, and the “step n size” > 0 is small and might go to zero as n??. In its simplest form, n ? is a parameter of a system, and the random vector Y is a function of n “noise-corrupted” observations taken on the system when the parameter is set to ? . One recursively adjusts the parameter so that some goal is met n asymptotically. Thisbookisconcernedwiththequalitativeandasymptotic properties of such recursive algorithms in the diverse forms in which they arise in applications. There are analogous continuous time algorithms, but the conditions and proofs are generally very close to those for the discrete time case. The original work was motivated by the problem of ?nding a root of a continuous function g ̄(?), where the function is not known but the - perimenter is able to take “noisy” measurements at any desired value of ?. Recursive methods for root ?nding are common in classical numerical analysis, and it is reasonable to expect that appropriate stochastic analogs would also perform well.