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Generic Uniform Convergence

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Author Info
Donald W.K. Andrews () (Cowles Foundation, Yale University)

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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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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 940.

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

Note: CFP 810.
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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
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Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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

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Cited by:
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  1. M. Hashem Pesaran & Yongcheol Shin, 2002. "Long-Run Structural Modelling," Econometric Reviews, Taylor and Francis Journals, vol. 21(1), pages 49-87. [Downloadable!] (restricted)
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