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Generalized Inverses and Asymptotic Properties of Wald Tests

Vuong, Quang H. (1986) Generalized Inverses and Asymptotic Properties of Wald Tests. Social Science Working Paper, 607. California Institute of Technology , Pasadena, CA. (Unpublished)

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We consider Wald tests based on consistent estimators of g-inverses of the asymptotic covariance matrix ∑ of a statistic that is n^1/2-asymptotically normal distributed under the null hypothesis. Under the null hypothesis and under any sequence of local alternatives in the column space of ∑, these tests are asymptotically equivalent for any choice of g-inverses. For sequences of local alternatives not in the column space of ∑ and for a suitable choice of g- inverse, the asymptotic power of the corresponding Wald test can be made equal to zero or arbitrarily large. In particular, the test based on a consistent estimator of the Moore-Penrose inverse of ∑ has zero asymptotic power against sequences of local alternatives in the orthogonal complement to the column space of ∑.

Item Type:Report or Paper (Discussion Paper)
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Additional Information:This research was supported by National Science Foundation Grant SES-8410593. I am indebted to D. Lien and D. Rivers for helpful discussion and to C. R. Jackson for moral support. Published as Vuong, Quang H. "Generalized inverses and asymptotic properties of Wald tests." Economics Letters 24.4 (1987): 343-347.
Group:Social Science Working Papers
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Subject Keywords:Generalized Inverses, Wald Tests, Asymptotic Power
Series Name:Social Science Working Paper
Issue or Number:607
Record Number:CaltechAUTHORS:20170913-143641248
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81423
Deposited By: Jacquelyn Bussone
Deposited On:15 Sep 2017 18:13
Last Modified:03 Oct 2019 18:42

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