Let us observe an infinite sequence $z_1 = r_1 + \varepsilon_1, z_2 = r_2 + \varepsilon_2, \cdots$ where $r_1, r_2,\cdots$ are the partial sums of independent and identically distributed random variables and the sequence of random variables $\varepsilon_k$ (the errors) is bounded by a function $f(k)$. Knowing the sequence $z_n$ we want to determine the distribution function of the summands. We will show that this problem cannot be solved in general even if $f(k)$ is constant.
Publié le : 1977-12-14
Classification:
Characteristic functions,
mixing of distributions,
partial sums of i.i.d. rv's,
Cauchy's coefficient estimation,
60G50,
62D05,
42A80
@article{1176995665,
author = {Halasz, G. and Major, P.},
title = {Reconstructing the Distribution from Partial Sums of Samples},
journal = {Ann. Probab.},
volume = {5},
number = {6},
year = {1977},
pages = { 987-998},
language = {en},
url = {http://dml.mathdoc.fr/item/1176995665}
}
Halasz, G.; Major, P. Reconstructing the Distribution from Partial Sums of Samples. Ann. Probab., Tome 5 (1977) no. 6, pp. 987-998. http://gdmltest.u-ga.fr/item/1176995665/