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Asymptotics for Semiparametric Econometric Models: I. Estimation


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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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Bibliographic Info

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

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Keywords: Asymptotic normality; empirical process; infinite dimensional nuisance parameter; Lagrange multiplier test; likelihood ratio-like test; nonparametric estimation; semiparametric estimation; semiparametric model; semiparametric test; stochastic equicontinuity; Wald test; weak convergence;


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Cited by:
  1. Gary Gorton & Richard Rosen, . "Corporate Control, Portfolio Choice, and the Decline of Banking," Rodney L. White Center for Financial Research Working Papers, Wharton School Rodney L. White Center for Financial Research 2-93, Wharton School Rodney L. White Center for Financial Research.
  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. 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.
  4. 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.


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