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Chapter 6: Monte Carlo Methods for Inferential Statistics 227

www.atri.curtin.edu.au/csp. It requires the MATLAB Statistics Tool-
box and has a postscript version of the reference manual.
Other software exists for Monte Carlo simulation as applied to statistics.
The Efron and Tibshirani [1993] book has a description of S code for imple-
menting the bootstrap. This code, written by the authors, can be downloaded
from the statistics archive at Carnegie-Mellon University that was mentioned
in Chapter 1. Another software package that has some of these capabilities is
called Resampling Stats® [Simon, 1999], and information on this can be
found at www.resample.com. Routines are available from Resampling Stats
for MATLAB [Kaplan, 1999] and Excel.

6.6 Further Reading

Mooney [1997] describes Monte Carlo simulation for inferential statistics that
is written in a way that is accessible to most data analysts. It has some excel-
lent examples of using Monte Carlo simulation for hypothesis testing using
multiple experiments, assessing the behavior of an estimator, and exploring
the distribution of a statistic using graphical techniques. The text by Gentle
[1998] has a chapter on performing Monte Carlo studies in statistics. He dis-
cusses how simulation can be considered as a scientific experiment and
should be held to the same high standards. Hoaglin and Andrews [1975] pro-
vide guidelines and standards for reporting the results from computations.
Efron and Tibshirani [1991] explain several computational techniques, writ-
ten at a level accessible to most readers. Other articles describing Monte
Carlo inferential methods can be found in Joeckel [1991], Hope [1968], Besag
and Diggle [1977], Diggle and Gratton [ 1984], Efron [1979], Efron and Gong
[1983], and Teichroew [1965].
There has been a lot of work in the literature on bootstrap methods. Per-
haps the most comprehensive and easy to understand treatment of the topic
can be found in Efron and Tibshirani [1993]. Efron’s [1982] earlier monogram
on resampling techniques describes the jackknife, the bootstrap and cross-
validation. A more recent book by Chernick [1999] gives an updated descrip-
tion of results in this area, and it also has an extensive bibliography (over
1,600 references!) on the bootstrap. Hall [1992] describes the connection
between Edgeworth expansions and the bootstrap. A volume of papers on
the bootstrap was edited by LePage and Billard [1992], where many applica-
tions of the bootstrap are explored. Politis, Romano, and Wolf [1999] present
subsampling as an alternative to the bootstrap. A subset of articles that
present the theoretical justification for the bootstrap are Efron [1981, 1985,
1987]. The paper by Boos and Zhang [2000] looks at a way to ease the compu-
tational burden of Monte Carlo estimation of the power of tests that uses res-
ampling methods. For a nice discussion on the coverage of the bootstrap
percentile confidence interval, see Polansky [1999].

© 2002 by Chapman & Hall/CRC