A Note on the Asymptotic Variance of Sample Roots

Timothy Halliday

No 201209, Working Papers from University of Hawaii at Manoa, Department of Economics

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.

Keywords: Principal Components Analysis; Asymptotic Distribution; Extremum Estimation (search for similar items in EconPapers)
JEL-codes: C01 C02 (search for similar items in EconPapers)
Pages: 14 pages
Date: 2012-06-01
New Economics Papers: this item is included in nep-ecm
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