James E. Gentle
Computational Statistics
by Springer

Preface
This book began as a revision of Elements of Computational Statistics, pub-
lished by Springer in 2002. That book covered computationally-intensive sta-
tistical methods from the perspective of statistical applications, rather than
from the standpoint of statistical computing.
Most of the students in my courses in computational statistics were in a
program that required multiple graduate courses in numerical analysis, and so
in my course in computational statistics, I rarely covered topics in numerical
linear algebra or numerical optimization, for example. Over the years, how-
ever, I included more discussion of numerical analysis in my computational
statistics courses. Also over the years I have taught numerical methods courses
with no or very little statistical content. I have also accumulated a number
of corrections and small additions to the elements of computational statistics.
The present book includes most of the topics from Elements and also incor-
porates this additional material. The emphasis is still on computationally-
intensive statistical methods, but there is a substantial portion on the numer-
ical methods supporting the statistical applications.
I have attempted to provide a broad coverage of the field of computational
statistics. This obviously comes at the price of depth.
Part I, consisting of one rather long chapter, presents some of the most
important concepts and facts over a wide range of topics in intermediate-level
mathematics, probability and statistics, so that when I refer to these concepts
in later parts of the book, the reader has a frame of reference.
Part I attempts to convey the attitude that computational inference, to-
gether with exact inference and asymptotic inference, is an important com-
ponent of statistical methods.
Many statements in Part I are made without any supporting argument,
but references and notes are given at the end of the chapter. Most readers
and students in courses in statistical computing or computational statistics
will be familiar with a substantial proportion of the material in Part I, but I
do not recommend skipping the chapter. If readers are already familiar with
the material, they should just read faster. The perspective in this chapter is