Approximated and Estimated Saddlepoint Approximations
Author : Pamela Ann Ohman
Publisher :
Page : 218 pages
File Size : 27,72 MB
Release : 1997
Category :
ISBN :
Author : Pamela Ann Ohman
Publisher :
Page : 218 pages
File Size : 27,72 MB
Release : 1997
Category :
ISBN :
Author : Ronald W. Butler
Publisher : Cambridge University Press
Page : 548 pages
File Size : 44,16 MB
Release : 2007-08-16
Category : Mathematics
ISBN : 1139466518
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 : 45,36 MB
Release : 1995
Category : Mathematics
ISBN : 9780198522959
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 : Ying-ming Jou
Publisher :
Page : 144 pages
File Size : 23,4 MB
Release : 1997
Category :
ISBN :
Author : Philippe Flajolet
Publisher : Cambridge University Press
Page : 825 pages
File Size : 15,96 MB
Release : 2009-01-15
Category : Mathematics
ISBN : 1139477161
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 : Marc Moore
Publisher : IMS
Page : 532 pages
File Size : 38,27 MB
Release : 2003
Category : Mathematical statistics
ISBN : 9780940600577
Author : Yue Kuen Kwok
Publisher : Springer
Page : 134 pages
File Size : 33,37 MB
Release : 2018-02-16
Category : Mathematics
ISBN : 3319741012
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 : Henry M. Streby
Publisher : CRC Press
Page : 246 pages
File Size : 20,95 MB
Release : 2016-10-26
Category : Nature
ISBN : 1315355639
Golden-winged Warblers (Vermivora chrysoptera) are migratory songbirds that breed in temperate North America, primarily in the Great Lakes region with remnant populations throughout the Appalachian Mountains, and winter in Central and northern South America. Their breeding range has contracted dramatically in the Appalachian Mountains and many populations have dramatically declined, likely due to habitat loss, competition and interbreeding with Blue-winged Warblers (Vermivora pinus), andglobal climate change.. As a result of population declines in much of the eastern portion of their breeding range, Golden-winged Warblers are listed as endangered or threatened in 10 U.S. states and in Canada and have been petitioned for protection under the U.S. Endangered Species Act. Published in collaboration with and on behalf of The American Ornithological Society, this volume in the highly-regarded Studies in Avian Biology series compiles extensive, current research on Golden-winged Warblers and summarizes what is known and identifies many remaining unknowns, providing a wealth of peer-reviewed science on which future research and listing decisions can be based.
Author : John E. Kolassa
Publisher : Springer Science & Business Media
Page : 194 pages
File Size : 49,14 MB
Release : 2013-04-17
Category : Mathematics
ISBN : 1475742770
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 sub ject, 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 on 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 : Stanislav Anatolyev
Publisher : CRC Press
Page : 230 pages
File Size : 44,69 MB
Release : 2011-06-07
Category : Business & Economics
ISBN : 1439838267
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.