INTRODUCTION 1) Introduction In 1979, Efron introduced the
bootstrap method as a kind of universal tool to obtain
approximation of the distribution of statistics. The now well known
underlying idea is the following : consider a sample X of Xl ' n
independent and identically distributed H.i.d.) random variables
(r. v,'s) with unknown probability measure (p.m.) P . Assume we are
interested in approximating the distribution of a statistical
functional T(P ) the -1 nn empirical counterpart of the functional
T(P) , where P n := n l:i=l aX. is 1 the empirical p.m. Since in
some sense P is close to P when n is large, n * * LLd. from P and
builds the empirical p.m. if one samples Xl ' ... , Xm n n -1 mn *
* P T(P ) conditionally on := mn l: i =1 a * ' then the behaviour
of P m n,m n n n X. 1 T(P ) should imitate that of when n and mn
get large. n This idea has lead to considerable investigations to
see when it is correct, and when it is not. When it is not, one
looks if there is any way to adapt it.
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