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Asymptotic Results for Generalized Wald Tests

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Abstract

This note presents conditions under which a quadratic form based on a g-inverted weighting matrix converges to a chi-square distribution as the sample size goes to infinity. Subject to fairly weak underlying conditions, a necessary and sufficient condition is given for this result. The result is of interest, because it is needed to establish asymptotic significance levels and local power properties of generalized Wald tests (i.e., Wald tests with singular limiting covariance matrices). Included in this class of tests are Hausman specification tests and various goodness of fit tests, among others. The necessary and sufficient condition is relevant to procedures currently in the econometrics literature, because it illustrates that some results stated in the literature only hold under more restrictive assumptions than those given.

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File URL: http://cowles.econ.yale.edu/P/cd/d07b/d0761-r.pdf
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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 761R.

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Length: 14 pages
Date of creation: Sep 1985
Date of revision: Apr 1986
Publication status: Published in Econometric Theory (1987), 3: 348-358
Handle: RePEc:cwl:cwldpp:761r

Note: CFP 694.
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Related research

Keywords: Generalized inverse; Wald test; asymptotics; chi-square;

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  1. Donald W.K. Andrews, 1985. "Random Cell Chi-Square Diagnostic Tests for Econometric Models: II. Theory," Cowles Foundation Discussion Papers 763R, Cowles Foundation for Research in Economics, Yale University, revised Jun 1986.
  2. Hausman, Jerry A. & Taylor, William E., 1981. "A generalized specification test," Economics Letters, Elsevier, vol. 8(3), pages 239-245.
  3. Donald W.K. Andrews, 1985. "Random Cell Chi-Square Diagnostic Tests for Econometric Models: I. Introduction and Applications," Cowles Foundation Discussion Papers 762, Cowles Foundation for Research in Economics, Yale University.
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