Geodesic
On convergence of the empirical mean method for non-identically distributed random vectors
E. Gordienko 1   ; J. Ruiz de Chávez 1   ; E. Zaitseva 2
1 Department of Mathematics Universidad Autónoma Metropolitana-Iztapalapa San Rafael Atlixco 186 Col. Vicentina C.P. 09340, Mexico City, México
2 Instituto Tecnológico Autónomo de México Rio Hondo 1 Col. Progreso Tizapan Del. Alvaro Obregón C.P. 01080, Mexico City, México
Applicationes Mathematicae, Tome 41 (2014) no. 1, pp. 1-12 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/am41-1-1
Keywords: consider following version standard problem empirical estimates stochastic optimization assume underlying random vectors independent necessarily identically distributed satisfy slow variation condition sense definition given paper these assumptions along usual restrictions boundedness equicontinuity class functions allow empirical mean method obtain consistent sequence estimates infimums functional minimized provide certain estimates rate convergence

E. Gordienko  1   ; J. Ruiz de Chávez  1   ; E. Zaitseva  2

1 Department of Mathematics Universidad Autónoma Metropolitana-Iztapalapa San Rafael Atlixco 186 Col. Vicentina C.P. 09340, Mexico City, México
2 Instituto Tecnológico Autónomo de México Rio Hondo 1 Col. Progreso Tizapan Del. Alvaro Obregón C.P. 01080, Mexico City, México 
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E. Gordienko; J. Ruiz de Chávez; E. Zaitseva. On convergence of the empirical mean method for non-identically distributed random vectors. Applicationes Mathematicae, Tome 41 (2014) no. 1, pp. 1-12. doi: 10.4064/am41-1-1

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