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Asymptotics for Semiparametric Econometric Models: I. Estimation

This paper provides a general framework for proving the square root of T consistency and asymptotic normality of a wide variety of semiparametric estimators. The results apply in time series and cross-sectional modeling contexts. The class of estimators considered consists of estimators that can be defined as the solution to a minimization problem based on a criterion function that may depend on a preliminary infinite dimensional nuisance parameter estimator. The criterion function need not be differentiable. The method of proof exploits results concerning the stochastic equicontinuity or weak convergence of normalized sums of stochastic processes. This paper also considers tests of nonlinear parametric restrictions in seimparametric econometric models. To date, only Wald tests of such restrictions have been considered in the literature. Here, Wald, Lagrange multiplier, and likelihood ratio-like tests statistics are considered. A general framework is provided for proving that these test statistics have asymptotic chi-square distributions under the null hypothesis and local alternatives. The results hold for a wide variety of underlying estimation techniques and in a wide variety of model scenarios.

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File URL: http://cowles.econ.yale.edu/P/cd/d09a/d0908-r.pdf
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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 908R.

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Length: 100 pages
Date of creation: 1989
Date of revision: Aug 1990
Publication status: Published in Econometrica (January 1994), 62(1): 43-72
Handle: RePEc:cwl:cwldpp:908r
Note: CFP 863.
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Web page: http://cowles.econ.yale.edu/

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Order Information: Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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