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

• Autorzy: E. Gordienko , J. Ruiz de Chávez , E. Zaitseva
• Języki publikacji: EN

Abstrakty

EN

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.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2014
• Tom: 41
• Numer: 1
• Strony: 1-12

Daty

wydano

2014

Twórcy

autor

E. Gordienko

• Department of Mathematics, Universidad Autónoma, Metropolitana-Iztapalapa, San Rafael Atlixco 186, Col. Vicentina, C.P. 09340, Mexico City, México

autor

J. Ruiz de Chávez

• Department of Mathematics, Universidad Autónoma, Metropolitana-Iztapalapa, San Rafael Atlixco 186, Col. Vicentina, C.P. 09340, Mexico City, México

autor

E. Zaitseva

• Instituto Tecnológico Autónomo, de México, Rio Hondo 1, Col. Progreso Tizapan, Del. Alvaro Obregón, C.P. 01080, Mexico City, México

Identyfikatory

DOI

10.4064/am41-1-1