Consistency in nonlinear econometric models: A generic uniform law of large numbers. (English) Zbl 0646.62101

A uniform law of large numbers (LLN) is a primary ingredient used in proving consistency of estimators in nonlinear econometric models. The purpose of this paper is to provide a generic uniform LLN that is sufficiently general to incorporate most applications of uniform LLNs in the nonlinear econometrics literature.
In summary, the paper presents a result that can be used to turn state of the art pointwise LLNs into uniform LLNs over compact sets with the addition of a single smoothness condition - a Lipschitz, derivative, or continuity condition. In contrast to other uniform LLNs that appear in the literature, the uniform LLN given here allows the full range of temporal dependence and heterogeneity of summands (i.e., nonidentical distibutions) that is available with pointwise LLNs.


62P20 Applications of statistics to economics
60F15 Strong limit theorems
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