The scaled-sample problem asks the following question: given a
distribution on a normed linear space E, when do there exist constants
${\gamma_n} such that $X^{(j)}/\gamma_n}_{j=1}^n$ converges as $n \to \infty$
(in the Hausdorff metric given by the norm) to a fixed set K? (Here
${X^{(j)}}$ are i.i.d. with the given distribution). The main result presented
here relates the convergence of scaled samples to a large deviation principle
for single observations, thereby achieving a dimension-free description of the
problem.
Publié le : 1996-07-14
Classification:
Scaled sample,
large deviations,
regular variation,
60G70,
60B12,
60B11,
60F15,
60D05
@article{1065725190,
author = {Pritchard, Geoffrey},
title = {On the convergence of scaled random samples},
journal = {Ann. Probab.},
volume = {24},
number = {2},
year = {1996},
pages = { 1490-1506},
language = {en},
url = {http://dml.mathdoc.fr/item/1065725190}
}
Pritchard, Geoffrey. On the convergence of scaled random samples. Ann. Probab., Tome 24 (1996) no. 2, pp. 1490-1506. http://gdmltest.u-ga.fr/item/1065725190/