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On the Formulation of Wald Tests of Nonlinear Restrictions

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Abstract

This paper utilizes asymptotic expansions to investigate alternative forms of the Ward set of nonlinear restrictions. Some formulae for the asymptotic expansion of the distribution of the Wald statistic are provided for a general case. When specialized to the simple cases that have been studied recently in the literature, these formulae are found to explain rather well the discrepancies in sampling behavior that have been observed by other authors. It is further shown how the correction delivered by the Edgeworth expansion may be used to find transformations of the restrictions which accelerate convergence to the asymptotic distribution.

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File URL: http://cowles.econ.yale.edu/P/cd/d08a/d0801.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 801.

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Length: 33 pages
Date of creation: Sep 1986
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Publication status: Published in Econometrica (September 1988), 56(5): 1065-1083
Handle: RePEc:cwl:cwldpp:801

Note: CFP 718.
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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
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Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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  1. Phillips, Peter C B, 1977. "A General Theorem in the Theory of Asymptotic Expansions as Approximations to the Finite Sample Distributions of Econometric Estimators," Econometrica, Econometric Society, vol. 45(6), pages 1517-34, September.
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