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A Note on the Asymptotic Variance of Sample Roots

Author

Listed:
  • Timothy Halliday

    (Department of Economics, University of Hawaii at Manoa)

Abstract

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 URL: http://www.economics.hawaii.edu/research/workingpapers/WP_12-9.pdf
    File Function: First version, 2012
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    More about this item

    Keywords

    Principal Components Analysis; Asymptotic Distribution; Extremum Estimation;
    All these keywords.

    JEL classification:

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

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    This paper has been announced in the following NEP Reports:

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