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On rank estimation in semidefinite matrices


  • Stephen G. Donald

    () (Department of Economics, University of Texas at Austin)

  • Natércia Fortuna

    () (CEF.UP, Universidade do Porto)

  • Vladas Pipiras

    () (University of North Carolina at Chapel Hill)


This work concerns the problem of rank estimation in semidefinite matrices, having either indefinite or semidefinite matrix estimator satisfying a typical asymptotic normality condition. Several rank tests are examined, based on either available rank tests or basic new results. A number of related issues are discussed such as the choice of matrix estimators and rank tests based on finer assumptions than those of asymptotic normality of matrix estimators. Several examples where rank estimation in semidefinite matrices is of interest are studied and serve as guide throughout the work.

Suggested Citation

  • Stephen G. Donald & Natércia Fortuna & Vladas Pipiras, 2010. "On rank estimation in semidefinite matrices," CEF.UP Working Papers 1002, Universidade do Porto, Faculdade de Economia do Porto.
  • Handle: RePEc:por:cetedp:1002

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    Cited by:

    1. Jin, Fei & Lee, Lung-fei, 2013. "Cox-type tests for competing spatial autoregressive models with spatial autoregressive disturbances," Regional Science and Urban Economics, Elsevier, vol. 43(4), pages 590-616.

    More about this item


    rank; symmetric matrix; indefinite and semidefinite estimators; eigenvalues; matrix decompositions; estimation; asymptotic normality.;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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