Applied Asymptotics Case Studies In Smallsample Statistics 1st Edition Brazzale Ar by Brazzale A.r., Davison A.c., Reid N. 9780521847032, 0521847036 instant download after payment.

In fields such as biology, medical sciences, sociology and economics researchers often

face the situation where the number of available observations, or the amount of available

information, is sufficiently small that approximations based on the normal distribution may

be unreliable. Theoretical work over the last quarter-century has led to new likelihoodbased

methods that yield very accurate approximations in finite samples, but this work

has had limited impact on statistical practice. This book illustrates by means of realistic

examples and case studies how to use the new theory, and investigates how and when it

makes a difference to the resulting inference. The treatment is oriented towards practice

and is accompanied by code in the R language which enables the methods to be applied in

a range of situations of interest to practitioners. The analysis includes some comparisons

of higher order likelihood inference with bootstrap and Bayesian methods.

--Preface--

The likelihood function plays a central role in both statistical theory and practice. Basic

results about likelihood inference, which we call first order asymptotics, were developed

in fundamental work by 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 so far been available. Our effort 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 hoa package bundle and

other materials may be obtained from the book’s web page

http://statwww.epfl.ch/AA