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Asymptotics for Semiparametric Econometric Models: I. Estimation

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Abstract

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.

Suggested Citation

  • Donald W.K. Andrews, 1989. "Asymptotics for Semiparametric Econometric Models: I. Estimation," Cowles Foundation Discussion Papers 908R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1990.
  • Handle: RePEc:cwl:cwldpp:908r
    Note: CFP 863.
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    File URL: http://cowles.yale.edu/sites/default/files/files/pub/d09/d0908-r.pdf
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    Cited by:

    1. Donald W.K. Andrews, 1992. "An Introduction to Econometric Applications of Functional Limit Theory for Dependent Random Variables," Cowles Foundation Discussion Papers 1020, Cowles Foundation for Research in Economics, Yale University.
    2. Whang, Yoon-Jae & Andrews, Donald W. K., 1993. "Tests of specification for parametric and semiparametric models," Journal of Econometrics, Elsevier, vol. 57(1-3), pages 277-318.
    3. Gorton, Gary & Rosen, Richard, 1995. " Corporate Control, Portfolio Choice, and the Decline of Banking," Journal of Finance, American Finance Association, vol. 50(5), pages 1377-1420, December.
    4. Delgado, Miguel A. & Robinson, Peter M., 1992. "Nonparametric and semiparametric methods for economic research," UC3M Working papers. Economics 2827, Universidad Carlos III de Madrid. Departamento de Economía.
    5. Donald W.K. Andrews & David Pollard, 1990. "A Functional Central Limit Theorem for Strong Mixing Stochastic Processes," Cowles Foundation Discussion Papers 951, Cowles Foundation for Research in Economics, Yale University.

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