TABLE OF CONTENTS The bootstrap does not always work. Examples of bootstrap failure have been reported from the very beginning of its development (Bickel and Freedman, 1981; Mammen, 1992; Young, 1994; Hu and Hu, 2000). Generally speaking, one cannot resample data which stems from a distribution with infinite variance. However, there is still some disagreement on this issue between statisticians (see work of Gine and Zinn (1989) versus that of Athreya (1987)).
Leaving this statistical polemic aside, from an engineering point of view we can assume that the bootstrap principle may not properly work with data that have an infinite variance, for example for ?-stable ( ? < 2) distributed data. As noted by Politis (1998), if we take a random sample 
= { X 1, , X n} from a standard Cauchy distribution, the bootstrap will behave erratically even for a large sample size. Other cases of failure are possible below we give a simple example.
Let X ~ 
(0, ?) and = { X 1, X 2, , X n}. Suppose we wish to estimate ? by 
and its distribution 
. The maximum likelihood estimator of ? is given by
To obtain an estimate of the density function of we sample with replacement from the data and each time estimate * from *. Alternatively, we could sample from (0, ) and...
