elements of distribution theory cambridge series in statistical and probabilistic mathematics

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Elements Of Distribution Theory

Author : Thomas A. Severini
ISBN : 9781139446112
Genre : Mathematics
File Size : 67. 1 MB
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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.

Distributions

Author : J.J. Duistermaat
ISBN : 0817646752
Genre : Mathematics
File Size : 84. 20 MB
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This textbook is an application-oriented introduction to the theory of distributions, a powerful tool used in mathematical analysis. The treatment emphasizes applications that relate distributions to linear partial differential equations and Fourier analysis problems found in mechanics, optics, quantum mechanics, quantum field theory, and signal analysis. The book is motivated by many exercises, hints, and solutions that guide the reader along a path requiring only a minimal mathematical background.

A User S Guide To Measure Theoretic Probability

Author : David Pollard
ISBN : 0521002893
Genre : Mathematics
File Size : 85. 92 MB
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This book grew from a one-semester course offered for many years to a mixed audience of graduate and undergraduate students who have not had the luxury of taking a course in measure theory. The core of the book covers the basic topics of independence, conditioning, martingales, convergence in distribution, and Fourier transforms. In addition there are numerous sections treating topics traditionally thought of as more advanced, such as coupling and the KMT strong approximation, option pricing via the equivalent martingale measure, and the isoperimetric inequality for Gaussian processes. The book is not just a presentation of mathematical theory, but is also a discussion of why that theory takes its current form. It will be a secure starting point for anyone who needs to invoke rigorous probabilistic arguments and understand what they mean.

Random Graph Dynamics

Author : Rick Durrett
ISBN : 9781139460880
Genre : Mathematics
File Size : 83. 23 MB
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The theory of random graphs began in the late 1950s in several papers by Erdos and Renyi. In the late twentieth century, the notion of six degrees of separation, meaning that any two people on the planet can be connected by a short chain of people who know each other, inspired Strogatz and Watts to define the small world random graph in which each site is connected to k close neighbors, but also has long-range connections. At a similar time, it was observed in human social and sexual networks and on the Internet that the number of neighbors of an individual or computer has a power law distribution. This inspired Barabasi and Albert to define the preferential attachment model, which has these properties. These two papers have led to an explosion of research. The purpose of this book is to use a wide variety of mathematical argument to obtain insights into the properties of these graphs. A unique feature is the interest in the dynamics of process taking place on the graph in addition to their geometric properties, such as connectedness and diameter.

Applied Asymptotics

Author : A. R. Brazzale
ISBN : 0521847036
Genre : Business & Economics
File Size : 67. 40 MB
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First practical treatment of small-sample asymptotics, enabling practitioners to apply new methods with confidence.

Asymptotic Statistics

Author : A. W. van der Vaart
ISBN : 0521784506
Genre : Mathematics
File Size : 27. 68 MB
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A mathematically rigorous, practical introduction presenting standard topics plus research.

Stochastic Processes

Author : Richard F. Bass
ISBN : 9781139501477
Genre : Mathematics
File Size : 24. 98 MB
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This comprehensive guide to stochastic processes gives a complete overview of the theory and addresses the most important applications. Pitched at a level accessible to beginning graduate students and researchers from applied disciplines, it is both a course book and a rich resource for individual readers. Subjects covered include Brownian motion, stochastic calculus, stochastic differential equations, Markov processes, weak convergence of processes and semigroup theory. Applications include the Black–Scholes formula for the pricing of derivatives in financial mathematics, the Kalman–Bucy filter used in the US space program and also theoretical applications to partial differential equations and analysis. Short, readable chapters aim for clarity rather than full generality. More than 350 exercises are included to help readers put their new-found knowledge to the test and to prepare them for tackling the research literature.

Statistical Models

Author : A. C. Davison
ISBN : 9781139437417
Genre : Mathematics
File Size : 45. 99 MB
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Models and likelihood are the backbone of modern statistics. This 2003 book gives an integrated development of these topics that blends theory and practice, intended for advanced undergraduate and graduate students, researchers and practitioners. Its breadth is unrivaled, with sections on survival analysis, missing data, Markov chains, Markov random fields, point processes, graphical models, simulation and Markov chain Monte Carlo, estimating functions, asymptotic approximations, local likelihood and spline regressions as well as on more standard topics such as likelihood and linear and generalized linear models. Each chapter contains a wide range of problems and exercises. Practicals in the S language designed to build computing and data analysis skills, and a library of data sets to accompany the book, are available over the Web.

Elements Of Large Sample Theory

Author : E.L. Lehmann
ISBN : 9780387227290
Genre : Mathematics
File Size : 87. 6 MB
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Written by one of the main figures in twentieth century statistics, this book provides a unified treatment of first-order large-sample theory. It discusses a broad range of applications including introductions to density estimation, the bootstrap, and the asymptotics of survey methodology. The book is written at an elementary level making it accessible to most readers.

From Finite Sample To Asymptotic Methods In Statistics

Author : Pranab K. Sen
ISBN : 9780521877220
Genre : Mathematics
File Size : 51. 26 MB
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A broad view of exact statistical inference and the development of asymptotic statistical inference.

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