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Generic Uniform Convergence

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Abstract

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 extend results 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 iid contexts, but which apply in dependent non-identically distributed contexts as well, and (4) they incorporate and extend the main results in the literature in a parsimonious fashion.

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File URL: http://cowles.econ.yale.edu/P/cd/d09a/d0940.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 940.

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Length: 21 pages
Date of creation: Mar 1990
Date of revision:
Publication status: Published in Econometric Theory (1992), 8: 241-257
Handle: RePEc:cwl:cwldpp:940

Note: CFP 810.
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Keywords: Consistency; law of large numbers; uniform convergence; asymptotic theory; test statistics; estimators;

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