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Pötscher, Benedikt M.; Prucha, Ingmar R.

Basic structure of the asymptotic theory in dynamic nonlinear econometric models. I: Consistency and approximation concepts. (English) Zbl 0737.62096

Econom. Rev. 10, No. 2, 125-216 (1991).
The paper reviews the current approaches in consistency and asymptotic normality of the \(M\)-estimators which are defined as the solution of a minimization or maximization problem, e.g. maximum likelihood estimators and generalized method of moments estimators. The typical proofs of consistency and asymptotic normality of \(M\)-estimators are uniform laws of large numbers (ULLNs) and central limit theorems (CLTs). As a result, the recent progress in the theory of inference in dynamic nonlinear econometric models builds on progress on the derivation of ULLNs and CLTs.
The basic method here is to show that the ULLNs and CLTs hold for functions of the data generating process by demonstrating that the functions of the data generating processes can be approximated by processes with a sufficiently fading memory, i.e. processes with \(\alpha\)-mixing or \(\phi\)-mixing dependence structure. A framework is developed for encompassing several different and at times rival approaches taken by Bierens and by Gallant, White and Wooldridge.
Reviewer: J.K.Sengupta (Santa Barbara)

Cited in 3 Reviews
Cited in 33 Documents

MSC:

62P20 Applications of statistics to economics

Keywords:

consistency; asymptotic normality; M-estimators; maximum likelihood estimators; generalized method of moments estimators; uniform laws of large numbers; central limit theorems; dynamic nonlinear econometric models; fading memory; dependence structure; least mean distance estimators; approximation concepts; mixing processes
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