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Tests of Rank

  • Robin, J.M.
  • Smith, R.J.

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.

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Paper provided by Faculty of Economics, University of Cambridge in its series Cambridge Working Papers in Economics with number 9521.

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Length: 31 pages
Date of creation: 1995
Date of revision:
Handle: RePEc:cam:camdae:9521
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