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A unifying theory of tests of rank.

Al-Sadoon, M. (2017) 'A unifying theory of tests of rank.', Journal of econometrics., 199 (1). pp. 49-62.


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.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Publisher statement:© 2017 This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Date accepted:31 March 2017
Date deposited:16 August 2018
Date of first online publication:17 April 2017
Date first made open access:17 April 2019

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