Page 239 - Computational Statistics Handbook with MATLAB

226 Computational Statistics Handbook with MATLAB

ated with an estimate, then those are more efficient than the bootstrap. In
what situations should the analyst use caution in applying the bootstrap?
One important assumption that underlies the theory of the bootstrap is the
notion that the empirical distribution function is representative of the true
population distribution. If this is not the case, then the bootstrap will not
yield reliable results. For example, this can happen when the sample size is
small or the sample was not gathered using appropriate random sampling
techniques. Chernick [1999] describes other examples from the literature
where the bootstrap should not be used. We also address a situation in Chap-
ter 7 where the bootstrap fails. This can happen when the statistic is non-
smooth, such as the median.

6.5 MATLAB Code
We include several functions with the Computational Statistics Toolbox that
implement some of the bootstrap techniques discussed in this chapter. These
are listed in Table 6.2. Like bootstrp, these functions have an input argu-
ment that specifies a MATLAB function that calculates the statistic.

A
B
A
T
T
L
E
L
B
L
A T T A B L B E E 6.2 6.2
E
6.2
6.2
List of MATLAB Functions for Chapter 6
Purpose MATLAB Function
General bootstrap: resampling, csboot
estimates of standard error and bias bootstrp
Constructing bootstrap confidence csbootint
Intervals csbooperint
csbootbca
As we saw in the examples, the MATLAB Statistics Toolbox has a function
called bootstrp that will return the bootstrap replicates from the input
argument bootfun (e.g., mean, std, var, etc.). It takes an input data set,
finds the bootstrap resamples, applies the bootfun to the resamples, and
stores the replicate in the first row of the output argument. The user can get
two outputs from the function: the bootstrap replicates and the indices that
correspond to the points selected in the resample.
There is a Bootstrap MATLAB Toolbox written by Zoubir and Iskander at
the Curtin University of Technology. It is available for download at

© 2002 by Chapman & Hall/CRC