Page 231 - Computational Statistics Handbook with MATLAB

218 Computational Statistics Handbook with MATLAB

thetab = skewness(xboot);
seb = std(thetab);
From this we get an estimated standard error in the skewness of 0.14. Efron
and Tibshirani [1993] recommend that one look at histograms of the boot-
ˆ
θ
strap replicates as a useful tool for understanding the distribution of . We
show the histogram in Figure 6.6.
The MATLAB Statistics Toolbox has a function called bootstrp that
returns the bootstrap replicates. We now show how to get the bootstrap esti-
mate of standard error using this function.
% Now show how to do it with MATLAB Statistics Toolbox
% function: bootstrp.
Bmat = bootstrp(B,'skewness',forearm);
% What we get back are the bootstrap replicates.
% Get an estimate of the standard error.
sebmat = std(Bmat);
Note that one of the arguments to bootstrp is a string representing the
function that calculates the statistics. From this, we get an estimated standard
error of 0.12.

2.5

2

1.5

1

0.5

0
−0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3

IG
F FI U URE G 6. RE 6. 6 6
F F II GU RE RE 6. 6. 6
GU
6
This is a histogram for the bootstrap replicates in Example 6.9. This shows the estimated
distribution of the sample skewness of the forearm data.

© 2002 by Chapman & Hall/CRC