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: Ronald W. Butler

Publisher: Cambridge University Press

ISBN: 9781139466516

Category: Mathematics

Page:

View: 754

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.

Coherent measures of risk. Mathematical Finance, 9:203–228, 1999. R. W. Butler
. Saddlepoint Approximations with Applications. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge University Press, Cambridge, 2007.

Author: Bruno Remillard

Publisher: CRC Press

ISBN: 9781439856956

Category: Business & Economics

Page: 496

View: 388

While many financial engineering books are available, the statistical aspects behind the implementation of stochastic models used in the field are often overlooked or restricted to a few well-known cases. Statistical Methods for Financial Engineering guides current and future practitioners on implementing the most useful stochastic models used in f

CAMBRIDGE SERIES IN STATISTICAL AND PROBABILISTIC MATHEMATICS
Editorial Board Z. Ghahramani (Department of Engineering, University of
Cambridge) R. ... Saddlepoint Approximations with Applications, by Ronald W.
Butler 23.

Author: Roman Vershynin

Publisher: Cambridge University Press

ISBN: 9781108244541

Category: Mathematics

Page:

View: 790

High-dimensional probability offers insight into the behavior of random vectors, random matrices, random subspaces, and objects used to quantify uncertainty in high dimensions. Drawing on ideas from probability, analysis, and geometry, it lends itself to applications in mathematics, statistics, theoretical computer science, signal processing, optimization, and more. It is the first to integrate theory, key tools, and modern applications of high-dimensional probability. Concentration inequalities form the core, and it covers both classical results such as Hoeffding's and Chernoff's inequalities and modern developments such as the matrix Bernstein's inequality. It then introduces the powerful methods based on stochastic processes, including such tools as Slepian's, Sudakov's, and Dudley's inequalities, as well as generic chaining and bounds based on VC dimension. A broad range of illustrations is embedded throughout, including classical and modern results for covariance estimation, clustering, networks, semidefinite programming, coding, dimension reduction, matrix completion, machine learning, compressed sensing, and sparse regression.

2 ) approximations compared to 50000 tilted bootstrap samples of size 20 from
an initial sample from exponential variables . ... DANIELS , H . E . and YOUNG , G
. A . ( 1991 ) Saddlepoint Approximation For the Studentized Mean , With an Application to the Bootstrap , Biometrika , 78 ... and their Application , Cambridge Series in Statistical and Probabilistic Mathematics , Cambridge University Press ,
UK .

CAMBRIDGE Outstanding Scholarship A First Course in Statistical Programming
with R W . ... Titles from the Cambridge Series in Statistical and Probabilistic Mathematics Proballistic Mathe Networks Optimisation and ... 99 : Pb : 978 - 0 -
521 - 68689 - 1 Saddlepoint Approximations with Applications Ronald W . Butler
$ 95 .

Daniels , H . E . ( 1954 ) , “ Saddlepoint Approximation in Statistics , ” Annals of Mathematical Statistics , 25 , 631 - 650 . - ( 1987 ) , “ Tail Probability Approximation , ” International Statistical Review , 55 , 37 – 48 . Davison , A . C . ,
and Hinkley , D . V . ( 1997 ) , Bootstrap Methods and Their Application , Cambridge , U . K . : Cambridge University Press . DiCiccio , T . J . , Martin , M . A .
, and Young , G . A ...

Edgeworth and saddle-point approximation with statistical applications. J. R.
Statist. Soc., B, 41 ... Cambridge: Cambridge University Press. DANIELS, H.E. (
1954). Saddlepoint approximations in statistics. Ann. Math. Statist, 25, 631-50.

On some classes of series used in mathematical statistics . Trans . 6th Congr .
Scand . Math . , 399 . CRAMÉR , H . ( 1928 ) . On the ... Cambridge Univ . ...
Lognormal Distributions : Theory and Applications . ... Advances in Probability
Distributions with Given Marginals , Beyond the Copulas . Kluwer , Dordrecht and
Boston . DANIELS , H . E . ( 1954 ) . Saddlepoint approximations in statistics . Ann
. Math .

Author: Alan Stuart

Publisher: Wiley

ISBN: 0340614307

Category: Mathematics

Page: 700

View: 259

This major revision contains a largely new chapter 7 providing an extensive discussion of the bivariate and multivariate versions of the standard distributions and families. Chapter 16 has been enlarged to cover mulitvariate sampling theory, an updated version of material previously found in the old Volume 3. The previous chapters 7 and 8 have been condensed into a single chapter providing an introduction to statistical inference. Elsewhere, major updates include new material on skewness and kurtosis, hazard rate distributions, the bootstrap, the evaluation of the multivariate normal integral and ratios of quadratic forms. This new edition includes over 200 new references, 40 new exercises and 20 further examples in the main text. In addition, all the text examples have been given titles and these are listed at the front of the book for easier reference.

Random Variables and Probability Distributions . Cambridge University Press .
CRAMÉR , H . ... Math . Soc . , 11 , 290 . DANIELS , H . E . ( 1954 ) . Saddlepoint approximations in statistics . Ann . Math . Stats . , 25 , 631 . DAs , S . C . ( 1956 ) .

Key ingredients in these extensions are ( a ) saddlepoint approximations for tail
probabilities or asymptotic " local densities ” ... It consists of two basic
components : ( i ) a normal approximation to the probability of Xc ( t ) exceeding
some high level ( depending on c ) ... and D . R . Cox , Edgeworth and saddlepoint approximations with statistical applications ( with discussion ) , J .
Roy . ... Cambridge Univ .

Author: Ka-Sing Lau

Publisher: American Mathematical Soc.

ISBN: UOM:39015075618416

Category: Mathematics

Page: 874

View: 232

This volume consists of the proceedings of the Third International Congress of Chinese Mathematicians, held at the Chinese University of Hong Kong in December 2004. The Congress brought together eminent Chinese and overseas mathematicians to discuss the latest developments in pure and applied mathematics. This two-part proceedings contains the contents of lectures given by the plenary speakers and the invited speakers--the major portion comprising new results--together with some expository and survey articles. Eleven major topics are treated: algebra, number theory and cryptography; algebraic geometry and algebraic topology; geometric analysis; complex analysis and complex geometry; harmonic analysis and functional analysis; applied mathematics; dynamical systems, fractals and wavelets; numerical analysis; PDE; probability, statistics, and financial mathematics; and education.

Introduction Cambridge University Press , Cambridge , 2004. x + 258 pp . ...
2005h : 60229 60J27 ( 92D25 , 93E11 ) - Partially observed space - time Markov
random fields and their applications . ... 2 , Agho , Kingsley ( with Dai , Wen ;
Robinson , John ) Empirical saddlepoint approximations of the Studentized ratio
and regression ... Cambridge Series in Statistical and Probabilistic Mathematics ,
Agliari ...

Oxford Univ. Press. [3] DANIELs, H. E. (1954). Saddlepoint approximations in statistics. Ann. Math. Statist. 25 631–650. ... Cambridge, Mass. [6] Johnson, N. L. (
1959). A proof of Wald's theorem on cumulative sums. Ann. Math. Statist. ... The
use of Green's functions in the study of bounded random walks with application to
queuing theory. J. Math. Phys. ... Ann. Math. Statist. 32 549–560. [14] RichTER, W
. (1957). Local limit theorems for large deviations. Theor. Probability Appl. 2 ...

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: Philippe Flajolet

Publisher: Cambridge University Press

ISBN: 9781139477161

Category: Mathematics

Page:

View: 880

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.

Topics covered in this volume (large deviations, differential geometry, asymptotic expansions, central limit theorems) give a full picture of the current advances in the application of asymptotic methods in mathematical finance, and thereby ...

Author: Peter K. Friz

Publisher: Springer

ISBN: 9783319116051

Category: Mathematics

Page: 590

View: 484

Topics covered in this volume (large deviations, differential geometry, asymptotic expansions, central limit theorems) give a full picture of the current advances in the application of asymptotic methods in mathematical finance, and thereby provide rigorous solutions to important mathematical and financial issues, such as implied volatility asymptotics, local volatility extrapolation, systemic risk and volatility estimation. This volume gathers together ground-breaking results in this field by some of its leading experts. Over the past decade, asymptotic methods have played an increasingly important role in the study of the behaviour of (financial) models. These methods provide a useful alternative to numerical methods in settings where the latter may lose accuracy (in extremes such as small and large strikes, and small maturities), and lead to a clearer understanding of the behaviour of models, and of the influence of parameters on this behaviour. Graduate students, researchers and practitioners will find this book very useful, and the diversity of topics will appeal to people from mathematical finance, probability theory and differential geometry.