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Stochastic Limit TheoryAn Introduction for Econometricians$
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James Davidson

Print publication date: 1994

Print ISBN-13: 9780198774037

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0198774036.001.0001

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Uniform Stochastic Convergence

Uniform Stochastic Convergence

Chapter:
(p.327) 21 Uniform Stochastic Convergence
Source:
Stochastic Limit Theory
Author(s):

James Davidson

Publisher:
Oxford University Press
DOI:10.1093/0198774036.003.0021

This chapter concerns random sequences of functions on metric spaces. The main issue is the distinction between convergence at all points of the space (pointwise) and uniform convergence, where limit points are also taken into account. The role of the stochastic equicontinuity property is highlighted. Generic uniform convergence conditions are given and linked to the question of uniform laws of large numbers.

Keywords:   analytic set, Glivenko‐Cantelli theorem, pointwise convergence, stochastic equicontinuity, uniform convergence, uniform law of large numbers

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