A Course in the Large Sample Theory of Statistical Inference / Edition 1

by W. Jackson Hall, David Oakes

Overview

This book provides an accessible but rigorous introduction to asymptotic theory in parametric statistical models. Asymptotic results for estimation and testing are derived using the “moving alternative” formulation due to R. A. Fisher and L. Le Cam. Later chapters include discussions of linear rank statistics and of chi-squared tests for contingency table analysis, including situations where parameters are estimated from the complete ungrouped data. This book is based on lecture notes prepared by the first author, subsequently edited, expanded and updated by the second author.

Key features:

• Succinct account of the concept of “asymptotic linearity” and its uses
• Simplified derivations of the major results, under an assumption of joint asymptotic normality
• Inclusion of numerical illustrations, practical examples and advice
• Highlighting some unexpected consequences of the theory
• Large number of exercises, many with hints to solutions

Some facility with linear algebra and with real analysis including ‘epsilon-delta’ arguments is required. Concepts and results from measure theory are explained when used. Familiarity with undergraduate probability and statistics including basic concepts of estimation and hypothesis testing is necessary, and experience with applying these concepts to data analysis would be very helpful.

Product Details

ISBN-13:	9781498726061
Publisher:	Taylor & Francis
Publication date:	12/14/2023
Series:	Chapman & Hall/CRC Texts in Statistical Science
Pages:	320
Product dimensions:	6.12(w) x 9.19(h) x (d)

About the Author

W. J. (“Jack”) Hall was Professor at the University of Rochester from 1969 to his death in 2012. He was instrumental in founding the graduate program in Statistics. His research interests included decision theory, survival analysis, semiparametric inference and sequential analysis. He worked with medical colleagues to develop innovative statistical designs for clinical trials in cardiology.

David Oakes is Professor and a former department chair at the University of Rochester. His areas of research interests include survival analysis and stochastic processes.

Table of Contents

Random Variables and Vectors Page. Weak Convergence Page. Asymptotic Linearity of Statistics Page. Local Analysis Page. Large-Sample Estimation Page. Large-Sample Hypothesis Testing and Confidence Sets Page. An Introduction to Rank Tests and Estimates Page. An Introduction to Multinomial Chi-square Tests Page.

Editorial Reviews

"Overall, the book is presented clearly, with an excellent sequence of concepts that guide the reader through the material effectively. I foundmost chapters engaging and detailed, offering a good balance of theory and application.[...] A Course in the Large Sample Theory of Statistical Inference is a comprehensive and accessible textbook, well-suited for a graduate-level course on large sample theory. Building on the concepts fromstandard/intermediate statistical inference courses, this book offers a smooth transition into the principles of large sample theory. It features simplified derivations of key results, along with numerical illustrations, practical examples,
and insightful guidance. This combination provides a strong foundation for graduate students, researchers, and practitioners who seek to apply these concepts to real-worlddata applications. Certainly suitable for a library purchase, and, definitely worthy of my office shelf!"
/-Indranil Sahoo, in The American Statistician, December 2024

From the Publisher