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A unifying theory of tests of rank

Al-Sadoon, M.

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The general principles underlying tests of matrix rank are investigated. It is demonstrated that statistics for such tests can be seen as implicit functions of null space estimators. In turn, the asymptotic behaviour of the null space estimators is shown to determine the asymptotic behaviour of the statistics through a plug-in principle. The theory simplifies the asymptotics under a variety of alternatives of empirical relevance as well as misspecification, clarifies the relationships between the various existing tests, makes use of important results in the numerical analysis literature, and motivates numerous new tests. A brief Monte Carlo study illustrates the results.

Journal Article Type Article
Acceptance Date Mar 31, 2017
Online Publication Date Apr 17, 2017
Publication Date Jul 1, 2017
Deposit Date Aug 15, 2018
Publicly Available Date Apr 17, 2019
Journal Journal of Econometrics
Print ISSN 0304-4076
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 199
Issue 1
Pages 49-62
Public URL


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