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TESTS OF RANK

Published online by Cambridge University Press:  01 April 2000

Jean-Marc Robin  and
Richard J. Smith
Jean-Marc Robin
Affiliation:
INRA and CREST-INSEE
Richard J. Smith
Affiliation:
University of Bristol
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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.

Type
Research Article
Information
Econometric Theory , Volume 16 , Issue 2 , April 2000 , pp. 151 - 175
Copyright
© 2000 Cambridge University Press

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