Introduction to Statistical Limit Theory

1. Auflage 2011
ISBN: 978-1-4200-7660-8
Verlag: Chapman and Hall/CRC

Buch, Englisch, 646 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 1124 g

Helping students develop a good understanding of asymptotic theory, Introduction to Statistical Limit Theory provides a thorough yet accessible treatment of common modes of convergence and their related tools used in statistics. It also discusses how the results can be applied to several common areas in the field.

The author explains as much of the background material as possible and offers a comprehensive account of the modes of convergence of random variables, distributions, and moments, establishing a firm foundation for the applications that appear later in the book. The text includes detailed proofs that follow a logical progression of the central inferences of each result. It also presents in-depth explanations of the results and identifies important tools and techniques. Through numerous illustrative examples, the book shows how asymptotic theory offers deep insight into statistical problems, such as confidence intervals, hypothesis tests, and estimation.

With an array of exercises and experiments in each chapter, this classroom-tested book gives students the mathematical foundation needed to understand asymptotic theory. It covers the necessary introductory material as well as modern statistical applications, exploring how the underlying mathematical and statistical theories work together.

Zielgruppe

Professional Practice & Development

Autoren/Hrsg.

Polansky, Alan M.

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung

Inhaltsverzeichnis

Sequences of Real Numbers and Functions. Random Variables and Characteristic Functions. Convergence of Random Variables. Convergence of Distributions. Convergence of Moments. Central Limit Theorems. Asymptotic Expansions for Distributions. Asymptotic Expansions for Random Variables. Differentiable Statistical Functionals. Parametric Inference. Nonparametric Inference. Appendices. References.

Über Autor(innen)

Alan M. Polansky is an associate professor in the Division of Statistics at Northern Illinois University. Dr. Polansky is the author of Observed Confidence Levels: Theory and Application (CRC Press, October 2007). His research interests encompass nonparametric statistics and industrial applications of statistics.