Although Normal Approximation and Asymptotic Expansions was first published in 1976, it has gained new significance and renewed interest among statisticians due to the developments of modern statistical techniques such as the bootstrap, the efficacy of which can be ascertained by asymptotic expansions.
This also is the only book containing a detailed treatment of various refinements of the multivariate central limit theorem (CLT), including Berryssen-type error bounds for probabilities of general classes of functions and sets, and asymptotic expansions for both lattice and non-lattice distributions. With meticulous care, the authors develop necessary background on
Eweak convergence theory,
EFourier analysis,
Egeometry of convex sets, and
Ethe relationship between lattice random vectors and discrete subgroups of Rk.
The formalism developed in the book has been used in the extension of the theory by Goetze and Hipp to sums of weakly dependent random vectors.
This edition of the book includes a new chapter that provides an application
of Stein's method of approximation to the multivariate CLT.
The book is appropriate for graduate students of probability and statistics as well as researchers in these and other fields whose work involves the asymptotic theory of statistics.
Preface to the Classics Edition;
Preface;
Chapter 1: Weak Convergence of Probability Measures and Uniformity Classes;
Chapter 2: Fourier Transforms and Expansions of Characteristic Functions;
Chapter 3: Bounds for Errors of Normal Approximation;
Chapter 4: Asymptotic Expansions-Nonlattice Distributions;
Chapter 5: Asymptotic Expansions-Lattice Distributions;
Chapter 6: Two Recent Improvements;
Chapter 7: An Application of Stein's Method;
Appendix A.1: Random Vectors and Independence;
Appendix A.2: Functions of Bounded Variation and Distribution Functions;
Appendix A.3: Absolutely Continuous, Singular, and Discrete Probability Measures;
Appendix A.4: The Euler-MacLaurin Sum Formula for Functions of Several Variables
References;
Index.
Hardback ISBN: 9781107005297
Paperback ISBN: 9780521183017
Series: London Mathematical Society Student Texts (No. 77)
50 exercises
Dimensions: 228 x 152 mm
Not yet published - available from March 2011
View other formats: Paperback
In this book, three authors introduce readers to strong approximation methods, analytic pro-p groups and zeta functions of groups. Each chapter illustrates connections between infinite group theory, number theory and Lie theory. The first explains how methods from linear algebraic groups can be utilised to study the finite images of linear groups. The second introduces the theory of compact p-adic analytic groups. The final chapter provides an overview of zeta functions associated to groups and rings. Derived from an LMS/EPSRC Short Course for graduate students, this book provides a concise introduction to a very active research area and assumes less prior knowledge than existing monographs or original research articles. Accessible to beginning graduate students in group theory, it will also appeal to researchers interested in infinite group theory and its interface with Lie theory and number theory.
* Exercises, some with solutions, provide a deeper understanding of the subject
* Numerous examples give the reader hands-on experience
* Suitable for self-study or seminar series and contains a guide to more advanced literature
ISBN: 978-0-470-28907-5
Hardcover
416 pages
December 2010
This book concerns the error in data collected using sample surveys, the nature and magnitudes of the errors, their effects on survey estimates, how to model and estimate the errors using a variety of modeling methods, and, finally, how to interpret the estimates and make use of the results in reducing the error for future surveys. The book focuses on models that are appropriate for categorical data, although there are references to the differences and special problems that arise in the analysis and modeling of error for continuous data. Though the primary modeling method that is described is latent class analysis (LCA), a wide range of related models and applications are also discussed.
ISBN: 978-0-470-50822-0
Hardcover
658 pages
November 2010
This book focuses on the comparison, contrast, and assessment of risks on the basis of clinical investigations. It develops basic concepts as well as deriving biostatistical methods through both the application of classical mathematical statistical tools and more modern likelihood-based theories.
The first half of the book presents methods for the analysis of single and multiple 2x2 tables for cross-sectional, prospective, and retrospective (case-control) sampling, with and without matching using fixed and two-stage random effects models.
The text then moves on to present a more modern likelihood- or model-based approach, which includes unconditional and conditional logistic regression; the analysis of count data and the Poisson regression model; the analysis of event time data, including the proportional hazards and multiplicative intensity models; and elements of categorical data analysis (expanded in this edition).
SAS subroutines are both showcased in the text and embellished online by way of a dedicated author website. The book contains a technical, but accessible appendix that presents the core mathematical statistical theory used for the development of classical and modern statistical methods.
ISBN: 978-3-527-40931-0
Hardcover
260 pages
March 2011
Written by recognized experts, this edited book covers recent theoretical, experimental and applied issues in the growing fi eld of Complex Systems and Nonlinear Dynamics. It is divided into two parts, with the first section application based, incorporating the theory of bifurcation analysis, numerical computations of instabilities in dynamical systems and discussing experimental developments. The second part covers the
broad category of statistical mechanics and dynamical systems. Several novel exciting theoretical and mathematical insights and their consequences are conveyed to the reader.
Part I
Coastal Morphodynamics
Long-lived Transients in Transitional Pipe Flow
Dynamics of Patterns with Delayed Feedback
Optical Delay Dynamics and its Applications
Symbolic Dynamics in Genetic Oscillation Patterns
Translocation Dynamics and Randomness
Part II
Entropy Production, the Breaking of Detailed Balance, and the Arrow of Time
Monodromy and the Complexity of Quantum Systems
Dynamics in Materials Science
Synchronization on the Circle
Conclusion from the Editors
Discussions Results of the Conference, Future Perspectives
144 pages | 216x138mm
978-0-19-959618-8 | Hardback | January 2011 (estimated)
Original monograph on the foundations of mathematics
The latest work by an award-winning philosopher of science
Written in an accessible and engaging style
Will appeal to mathematicians and logicians as well as philosophers
Mathematics depends on proofs, and proofs must begin somewhere, from some fundamental assumptions. For nearly a century, the axioms of set theory have played this role, so the question of how these axioms are properly judged takes on a central importance. Approaching the question from a broadly naturalistic or second-philosophical point of view, Defending the Axioms isolates the appropriate methods for such evaluations and investigates the ontological and epistemological backdrop that makes them appropriate. In the end, a new account of the objectivity of mathematics emerges, one refreshingly free of metaphysical commitments.
Scholars and advanced students of philosophy of mathematics, philosophy of science, logic, and set theory.
Introduction
1: The Problem
2: Proper Method
3: Thin Realism
4: Arealism
5: Morals
Bibliography