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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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
Cited by: (explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)
M. Hashem Pesaran & Yongcheol Shin, 2002.
"Long-Run Structural Modelling,"
Econometric Reviews,
Taylor and Francis Journals, vol. 21(1), pages 49-87.
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