W. Jackson Hall & David (University of Rotchester, Rotchester, NY, USA) Oakes 
A Course in the Large Sample Theory of Statistical Inference [PDF ebook] 

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.