Tests of Rank
AbstractThis 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.
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Bibliographic InfoPaper provided by Faculty of Economics, University of Cambridge in its series Cambridge Working Papers in Economics with number 9521.
Length: 31 pages
Date of creation: 1995
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