Tests of rank

Jean-Marc Robin and Richard J. Smith

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Abstract: This paper considers tests for the rank of a matrix for which a root-T consistent estimator is available. However, in contrast to tests associated with the minimum chi-square and asymptotic least squares principles, the estimator's asymptotic variance matrix is not required to be either full or of known rank. Test statistics based on certain estimated characteristic roots are proposed whose limiting distributions are a weighted sum of independent chi-squared variables. These weights may be simply estimated, yielding convenient estimators for the limiting distributions of the proposed statistics. A sequential testing procedure is presented that yields a consistent estimator for the rank of a matrix. A simulation experiment is conducted comparing the characteristic root statistics advocated in this paper with statistics based on the Wald and asymptotic least squares principles.

Keywords: Ranks (search for similar items in EconPapers)
Date: 2000
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Citations: View citations in EconPapers (92)

Published in Econometric Theory, 2000, 16 (2), pp.151-175. ⟨10.1017/S0266466600162012⟩

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Related works:
Journal Article: TESTS OF RANK (2000)
Working Paper: Tests of rank (2000)
Working Paper: Tests of Rank (1995)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00357758

DOI: 10.1017/S0266466600162012

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