Page 17 - Computational Statistics Handbook with MATLAB

2 Computational Statistics Handbook with MATLAB

gain some useful information from them. In contrast, the traditional
approach has been to first design the study based on research questions and
then collect the required data.
Because the storage and collection is so cheap, the data sets that analysts
must deal with today tend to be very large and high-dimensional. It is in sit-
uations like these where many of the classical methods in statistics are inad-
equate. As examples of computational statistics methods, Wegman [1988]
includes parallel coordinates for high dimensional data representation, non-
parametric functional inference, and data set mapping where the analysis
techniques are considered fixed.
Efron and Tibshirani [1991] refer to what we call computational statistics as
computer-intensive statistical methods. They give the following as examples for
these types of techniques: bootstrap methods, nonparametric regression,
generalized additive models and classification and regression trees. They
note that these methods differ from the classical methods in statistics because
they substitute computer algorithms for the more traditional mathematical
method of obtaining an answer. An important aspect of computational statis-
tics is that the methods free the analyst from choosing methods mainly
because of their mathematical tractability.
Volume 9 of the Handbook of Statistics: Computational Statistics [Rao, 1993]
covers topics that illustrate the “... trend in modern statistics of basic method-
ology supported by the state-of-the-art computational and graphical facili-
ties...” It includes chapters on computing, density estimation, Gibbs
sampling, the bootstrap, the jackknife, nonparametric function estimation,
statistical visualization, and others.
We mention the topics that can be considered part of computational statis-
tics to help the reader understand the difference between these and the more
traditional methods of statistics. Table 1.1 [Wegman, 1988] gives an excellent
comparison of the two areas.

1.2 An Overview of the Book

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The focus of this book is on methods of computational statistics and how to
implement them. We leave out much of the theory, so the reader can concen-
trate on how the techniques may be applied. In many texts and journal arti-
cles, the theory obscures implementation issues, contributing to a loss of
interest on the part of those needing to apply the theory. The reader should
not misunderstand, though; the methods presented in this book are built on
solid mathematical foundations. Therefore, at the end of each chapter, we

© 2002 by Chapman & Hall/CRC