On convergence of the empirical mean method for non-identically distributed random vectors

E. Gordienko, J. Ruiz de Chávez, and E. Zaitseva. "On convergence of the empirical mean method for non-identically distributed random vectors." Applicationes Mathematicae 41.1 (2014): 1-12. <http://eudml.org/doc/279930>.

@article{E2014,
abstract = {We consider the following version of the standard problem of empirical estimates in stochastic optimization. We assume that the underlying random vectors are independent and not necessarily identically distributed but that they satisfy a "slow variation" condition in the sense of the definition given in this paper. We show that these assumptions along with the usual restrictions (boundedness and equicontinuity) on a class of functions allow one to use the empirical mean method to obtain a consistent sequence of estimates of infimums of the functional to be minimized. Also, we provide certain estimates of the rate of convergence.},
author = {E. Gordienko, J. Ruiz de Chávez, E. Zaitseva},
journal = {Applicationes Mathematicae},
keywords = {stochastic optimization; empirical distributions; probability metrics; slowly varying measures; consistent estimates; rate of convergence},
language = {eng},
number = {1},
pages = {1-12},
title = {On convergence of the empirical mean method for non-identically distributed random vectors},
url = {http://eudml.org/doc/279930},
volume = {41},
year = {2014},
}

TY - JOUR
AU - E. Gordienko
AU - J. Ruiz de Chávez
AU - E. Zaitseva
TI - On convergence of the empirical mean method for non-identically distributed random vectors
JO - Applicationes Mathematicae
PY - 2014
VL - 41
IS - 1
SP - 1
EP - 12
AB - We consider the following version of the standard problem of empirical estimates in stochastic optimization. We assume that the underlying random vectors are independent and not necessarily identically distributed but that they satisfy a "slow variation" condition in the sense of the definition given in this paper. We show that these assumptions along with the usual restrictions (boundedness and equicontinuity) on a class of functions allow one to use the empirical mean method to obtain a consistent sequence of estimates of infimums of the functional to be minimized. Also, we provide certain estimates of the rate of convergence.
LA - eng
KW - stochastic optimization; empirical distributions; probability metrics; slowly varying measures; consistent estimates; rate of convergence
UR - http://eudml.org/doc/279930
ER -