A Course in the Large Sample Theory of Statistical Inference

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.