Page 18 - Computational Statistics Handbook with MATLAB

Chapter 1: Introduction 3

T
T
A B T T A B E L E L LE L E 1.1 1.1
AB
1.1
1.1
AB
Comparison Between Traditional Statistics and Computational Statistics
[Wegman, 1988]. Reprinted with permission from the Journal of the
Washington Academy of Sciences.
Traditional Statistics Computational Statistics
Small to moderate sample size Large to very large sample size
Independent, identically distributed Nonhomogeneous data sets
data sets
One or low dimensional High dimensional
Manually computational Computationally intensive

Mathematically tractable Numerically tractable
Well focused questions Imprecise questions

Strong unverifiable assumptions: Weak or no assumptions:
Relationships (linearity, additivity) Relationships (nonlinearity)
Error structures (normality) Error structures (distribution free)

Statistical inference Structural inference
Predominantly closed form Iterative algorithms possible
algorithms
Statistical optimality Statistical robustness

include a section containing references that explain the theoretical concepts
associated with the methods covered in that chapter.

Wh
Wh a t t a Cover CovereCovere e I Issd d Covere
WhWh
I
Issdd
aatt
In this book, we cover some of the most commonly used techniques in com-
putational statistics. While we cannot include all methods that might be a
part of computational statistics, we try to present those that have been in use
for several years.
Since the focus of this book is on the implementation of the methods, we
include algorithmic descriptions of the procedures. We also provide exam-
ples that illustrate the use of the algorithms in data analysis. It is our hope
that seeing how the techniques are implemented will help the reader under-
stand the concepts and facilitate their use in data analysis.
Some background information is given in Chapters 2, 3, and 4 for those
who might need a refresher in probability and statistics. In Chapter 2, we dis-
cuss some of the general concepts of probability theory, focusing on how they

© 2002 by Chapman & Hall/CRC