applied asymptotics

Applied Asymptotics

Case Studies in Small-Sample Statistics

by A. R. Brazzale, A. C. Davison and N. Reid
(Cambridge University Press, 2007)
Description and Reviews Table of Contents Errata Corrige
Answers to Exercises and Problems Software and Datasets On-line Complements
Author Information Publisher's Web Site Cover and Sample Pages



The likelihood function plays a central role in both statistical theory and practice, and every day it forms the basis of thousands, even millions, of inferences from data. Basic results about likelihood inference, which we call first order asymptotics, were developed in fundamental work by Sir R. A. Fisher during the 1920s, and now form an essential and widely taught part of both elementary and advanced courses in statistics. It is less well known that Fisher later proposed a more refined approach, which has been developed over the past three decades into a theory of higher order asymptotics. While this theory leads to some extremely accurate methods for parametric inference, accounts of the theory can appear forbidding, and the results may be thought to have little importance for statistical practice.

The purpose of this book is dispel this view, showing how higher order asymptotics may be applied in realistic examples with very little more effort than is needed for first order procedures, and to compare the resulting improved inferences with those from other approaches. To do this we have collected a range of examples and case studies, provided details on the implementation of higher order approximations, and compared the resulting inference to that based on other methods; usually first order likelihood theory, but where appropriate also methods based on simulation. Our examples are nearly all derived from regression models for discrete or continuous data, but range quite widely over the types of models and inference problems where likelihood methods are applied.

In order to make higher order methods accessible, we have striven for as simple an exposition as we thought feasible, aiming for heuristic explanation rather than full mathematical rigour. We do not presuppose previous knowledge of higher order asymptotics, key aspects of which are explained early in the book. The reader is assumed to have knowledge of basic statistics including some central classes of models, and some experience of standard likelihood methods in practice. We intend that the book be useful for students of statistics, practising statisticians and data analysts, as well as researchers interested in a more applied account of the methods than has been available to date. The theory has been made practicable by software developed by Alessandra Brazzale and Ruggero Bellio over many years, of which the hoa package bundle now available in R is the culmination. This software is extensively used throughout the book, and the ideas behind the hoa packages, described in Chapter 9, formed the basis for our approaches to programming when new software was needed for some of the examples.

The code and data sets used in this book are provided here.

Reviews of the book.

Table of Contents

1. Introduction
2. Uncertainty and approximation
3. Simple illustrations
4. Discrete data
5. Regression with continuous responses
6. Some case studies
7. Further topics
8. Likelihood approximations
9. Numerical implementations
10. Problems and further results
Some numerical techniques

Errata Corrige

Errata list in PDF available here (< 100Kb).

Viewer can be downloaded from

Answers to Exercises and Problems


On-line Complements


Author Information

Professor Brazzale is Associate Professor of Statistics at the University of Padova. She actively collaborates with the Institute for Biomedical Engineering of the Italian National Research Council, which kindly hosts this web page. Her current fields of interest include small-sample parametric inference, implementation of statistical software and modelling issues in environmental epidemiology and ecotoxicology.

Professor Davison holds the Chair of Statistics at the Swiss Federal Institute of Technology Lausanne. He is coauthor with Professor D. V. Hinkley of Bootstrap Methods and Their Application (1997), and author of Statistical Models (2003), published by Cambridge University Press. A profile is available here.

Professor Reid holds the Canada Research Chair in Statistical Theory and Applications at the University of Toronto. Her main area of research is theoretical statistics; her current fields of interest include aspects of environmental epidemiology and of high energy physics. She authored and coauthored many papers and several books. Her curriculum vitae is available here.

Questions or comments regarding the book should be addressed to:

Professor A. R. Brazzale
Dipartimento di Scienze Statistiche
Università degli Studi di Padova
Via Cesare Battisti 241/243
35121 Padova (PD)
    Professor A. C. Davison
Institute of Mathematics
École Polytechnique Fédérale de Lausanne
1015 Lausanne (VD)

Professor N. Reid
Department of Statistics
University of Toronto

Toronto, Ontario

Publisher's Web Site

How to order this book from Cambridge University Press.

Cover and Sample Pages

Image of Cover

Cambridge University Press. ISBN-13: 9780521847032 | ISBN-10: 0521847036, 2007.

45 line diagrams 4 half-tones 47 tables 69 exercises 

An excerpt is available here in PDF format.


Last updated on November 30, 2011