Synopses & Reviews
Synopsis
This book is based on detailed notes prepared by Professor Hall for his signature class on large sample theory in parametric models, which he taught at the University of Rochester for many years, most recently in 2012. It provides a rigorous but accessible introduction to the topic, using the moving alternative formulation developed by LeCam, but requiring a minimum of mathematical prerequisites. The book includes ideas and insights from Professor Hall's distinguished research career. It also includes many practical examples.
Synopsis
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. The book is based on lecture notes prepared by the first author, subsequently edited, expanded and updated by the second author.
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 of 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.
Synopsis
This book provides an accessible but rigorous introduction to asymptotic theory in parametric statistical models. The book is based on lecture notes prepared by the first author, subsequently edited, expanded and updated by the second author. Includes a large number of exercises.