Page 266 - Computational Statistics Handbook with MATLAB

254 Computational Statistics Handbook with MATLAB

will implement the jackknife procedure for estimating the bias and standard
error in an estimate. We also provide a function called csjackboot that will
implement the jackknife-after-bootstrap. These functions are summarized in
Table 7.1.
The cross-validation method is application specific, so users must write
their own code for each situation. For example, we showed in this chapter
how to use cross-validation to help choose a model in regression by estimat-
ing the prediction error. In Chapter 9, we illustrate two examples of cross-val-
idation: 1) to choose the right size classification tree and 2) to assess the
misclassification error. We also describe a procedure in Chapter 10 for using
K-fold cross-validation to choose the right size regression tree.

T
A
A
TA AB BL L L E 7.1 7.1
T
T
B
E
7.1
7.1
B
LE
E
List of Functions from Chapter 7 Included in the
Computational Statistics Toolbox.
Purpose MATLAB Function
Implements the jackknife and returns csjack
the jackknife estimate of standard
error and bias.
confidence csbootbca
Returns the bootstrap BC a
interval.
Implements the jackknife-after- csjackboot
bootstrap and returns the jackknife
estimate of the error in the bootstrap.

7.7 Further Reading
There are very few books available where the cross-validation technique is
the main topic, although Hjorth [1994] comes the closest. In that book, he dis-
cusses the cross-validation technique and the bootstrap and describes their
use in model selection. Other sources on the theory and use of cross-valida-
tion are Efron [1982, 1983, 1986] and Efron and Tibshirani [1991, 1993]. Cross-
validation is usually presented along with the corresponding applications.
For example, to see how cross-validation can be used to select the smoothing
parameter in probability density estimation, see Scott [1992]. Breiman, et al.
[1984] and Webb [1999] describe how cross-validation is used to choose the
right size classification tree.
The initial jackknife method was proposed by Quenouille [1949, 1956] to
estimate the bias of an estimate. This was later extended by Tukey [1958] to
estimate the variance using the pseudo-value approach. Efron [1982] is an

© 2002 by Chapman & Hall/CRC