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A Note on the Asymptotic Variance of Sample Roots


  • Timothy Halliday

    () (Department of Economics, University of Hawaii at Manoa)


We derive the asymptotic distribution of the eigenvalues of a sample covari- ance matrix with distinct roots. Our theorem can accommodate the situation in which the population covariance matrix is estimated via its sample analogue as well as the more general case in which it is estimated via a pN-consistent extremum estimator. The sample roots will have a Normal distribution in a large sample with a covariance matrix that is easy to compute. We con- duct Monte Carlo experiments that show that standard errors based on our derived asymptotic distribution accurately approximate standard errors in the empirical distribution.

Suggested Citation

  • Timothy Halliday, 2012. "A Note on the Asymptotic Variance of Sample Roots," Working Papers 201209, University of Hawaii at Manoa, Department of Economics.
  • Handle: RePEc:hai:wpaper:201209

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    File Function: First version, 2012
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    More about this item


    Principal Components Analysis; Asymptotic Distribution; Extremum Estimation;

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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