A note on uniform exponential convergence of sample average approximation of random functions
A note on uniform exponential convergence of sample average approximation of random functions
Shapiro and Xu [18] investigated uniform large deviation of a class of HÄolder continuous random functions. It is shown under some standard moment conditions that with probability approaching one at exponential rate with the increase of sample size, the sample average approximation of the random function converges to its expected value uniformly over a compact set. This note extends the result to a class of discontinuous functions whose expected values are continuous and the HÄolder continuity may be violated for some negligible random realizations. The extension entails the application of the exponential convergence result to a substantially larger class of practically interesting functions in stochastic optimization.
Sun, Hailin
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Xu, Huifu
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Sun, Hailin
eee2e5fb-018b-45d4-b599-08209509663c
Xu, Huifu
d3200e0b-ad1d-4cf7-81aa-48f07fb1f8f5
Sun, Hailin and Xu, Huifu
(2011)
A note on uniform exponential convergence of sample average approximation of random functions.
Journal of Mathematical Analysis and Applications.
(In Press)
Abstract
Shapiro and Xu [18] investigated uniform large deviation of a class of HÄolder continuous random functions. It is shown under some standard moment conditions that with probability approaching one at exponential rate with the increase of sample size, the sample average approximation of the random function converges to its expected value uniformly over a compact set. This note extends the result to a class of discontinuous functions whose expected values are continuous and the HÄolder continuity may be violated for some negligible random realizations. The extension entails the application of the exponential convergence result to a substantially larger class of practically interesting functions in stochastic optimization.
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Accepted/In Press date: January 2011
Organisations:
Operational Research
Identifiers
Local EPrints ID: 182203
URI: http://eprints.soton.ac.uk/id/eprint/182203
ISSN: 0022-247X
PURE UUID: 563e9c07-f116-43f8-8c3a-2195ab204af4
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Date deposited: 27 Apr 2011 15:04
Last modified: 15 Mar 2024 03:15
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Author:
Hailin Sun
Author:
Huifu Xu
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