Asymptotic distribution theorems in probability and statistics have always depended on the classical theory of weak convergence of distribution functions in Euclidean space - convergence, at continuity points of the limit function. The 20th century has seen the creation and extensive application of a more inclusive theory of weak convergence of probability measures on metric spaces. There are many asymptotic results that can be formulated within this classical theory but require, for their proofs, this more general theory, which thus does not merely study itself.

A one-stop reference to fractional factorials and related orthogonal arrays.

Presenting one of the most dynamic areas of statistical research, this book offers a systematic, rigorous, and up-to-date treatment of fractional factorial designs and related combinatorial mathematics. Leading statisticians Aloke Dey and Rahul Mukerjee consolidate vast amounts of material from the professional literature--expertly weaving fractional replication, orthogonal arrays, and optimality aspects. They develop the basic theory of fractional factorials using the calculus of factorial arrangements,...

A comprehensive introduction to the central limit theory-from foundations to current research
This volume provides an introduction to the central limit theory of random vectors, which lies at the heart of probability and statistics. The authors develop the central limit theory in detail, starting with the basic constructions of modern probability theory, then developing the fundamental tools of infinitely divisible distributions and regular variation. They provide a number of extensions and applications to probability and statistics, and take the reader through the fundamentals to the...

Foundations of time series for researchers and students

This volume provides a mathematical foundation for time series analysis and prediction theory using the idea of regression and the geometry of Hilbert spaces. It presents an overview of the tools of time series data analysis, a detailed structural analysis of stationary processes through various reparameterizations employing techniques from prediction theory, digital signal processing, and linear algebra. The author emphasizes the foundation and structure of time series and backs up this coverage with theory and...

This highly acclaimed text, now available in paperback, provides a thorough account of key concepts and theoretical results, with particular emphasis on viewing statistical inference as a special case of decision theory. Information-theoretic concepts play a central role in the development of the theory, which provides, in particular, a detailed discussion of the problem of specification of so-called prior ignorance . The work is written from the authors s committed Bayesian perspective, but an overview of non-Bayesian theories is also provided, and each chapter contains a wide-ranging...