A Course in the Large Sample Theory of Statistical Inference

W. Jackson Hall, David Oakes (University of Rotchester, Rotchester, NY, USA)

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English

Chapman & Hall/CRC
14 December 2023

Econometrics; Economic statistics; Probability & statistics

Series: Chapman & Hall/CRC Texts in Statistical Science

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.

By: W. Jackson Hall, David Oakes (University of Rotchester, Rotchester, NY, USA)
Imprint: Chapman & Hall/CRC
Country of Publication: United States
Dimensions: Height: 234mm, Width: 156mm,
Weight: 750g
ISBN: 9781498726061
ISBN 10: 1498726062
Series: Chapman & Hall/CRC Texts in Statistical Science
Pages: 310
Publication Date: 14 December 2023
Audience: College/higher education , Primary
Format: Hardback
Publisher's Status: Active

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.

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.