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Asymptotic Results for Generalized Wald Tests

Published online by Cambridge University Press:  11 February 2009

Donald W. K. Andrews
Donald W. K. Andrews
Affiliation:
Cowles Foundation for Research in Economics, Yale University
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Abstract

This paper 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.

Type
Research Article
Information
Econometric Theory , Volume 3 , Issue 3 , June 1987 , pp. 348 - 358
Copyright
Copyright © Cambridge University Press 1987

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