Uniform Convergence in Probability and Stochastic Equicontinuity

Econometrica ◽  
1991 ◽  
Vol 59 (4) ◽  
pp. 1161 ◽  
Author(s):  
Whitney K. Newey
Keyword(s):  
Uniform Convergence ◽  
Convergence In Probability ◽  
Stochastic Equicontinuity

scholarly journals Generic Uniform Convergence

1992 ◽  
Vol 8 (2) ◽  
pp. 241-257 ◽  
Author(s):  
Donald W.K. Andrews
Keyword(s):  
Uniform Convergence ◽  
Asymptotic Properties ◽  
Convergence In Probability ◽  
Test Statistics ◽  
Parameter Spaces ◽  
Totally Bounded ◽  
Convergence Results ◽  
Large Numbers ◽  
Uniform Law ◽  
Convergence Almost Surely

This paper presents several generic uniform convergence results that include generic uniform laws of large numbers. These results provide conditions under which pointwise convergence almost surely or in probability can be strengthened to uniform convergence. The results are useful for establishing asymptotic properties of estimators and test statistics.The results given here have the following attributes, (1) they extendresults of Newey to cover convergence almost surely as well as convergence in probability, (2) they apply to totally bounded parameter spaces (rather than just to compact parameter spaces), (3) they introduce a set of conditions for a generic uniform law of large numbers that has the attribute of giving the weakest conditions available for i.i.d. contexts, but which apply in some dependent nonidentically distributed contexts as well, and (4) they incorporate and extend themain results in the literature in a parsimonious fashion.

Uniform Stochastic Convergence

2021 ◽  
pp. 471-492
Author(s):  
James Davidson
Keyword(s):  
Uniform Convergence ◽  
Metric Spaces ◽  
Main Issue ◽  
Stochastic Convergence ◽  
Convergence Conditions ◽  
Laws Of Large Numbers ◽  
Random Sequences ◽  
Large Numbers ◽  
Stochastic Equicontinuity

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.

QUASI-UNIFORM CONVERGENCE AND ℒ-SPACES

1992 ◽  
Vol 18 (2) ◽  
pp. 321 ◽  
Author(s):  
Bukovská ◽  
Bukovský ◽  
Ewert
Keyword(s):  
Uniform Convergence

Topologies Between Compact and Uniform Convergence on Function Spaces, II

1992 ◽  
Vol 18 (1) ◽  
pp. 176 ◽  
Author(s):  
Kundu ◽  
McCoy ◽  
Raha
Keyword(s):  
Uniform Convergence ◽  
Function Spaces
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