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Biometrika 1976 63(3):639-645; doi:10.1093/biomet/63.3.639
© 1976 by Biometrika Trust
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Asymptotic distribution of the sample roots for a nonnormal population

CHRISTINE M. WATERNAUX

Department of Statistics, University of Michigan Ann Arbor

The distribution of the characteristic roots of the sample covariance matrix is studied for multivariate populations with finite fourth cumulants. For large sample sizes, the asymptotic forms of the marginal and joint distributions are given. For moderate and small sample sizes, empirical sampling techniques are used: various trivariate models are simulated, and the distributions of the sample roots are empirically observed. It is shown that the distributional results for a multivariate normal population are nonrobust to departures from normality; they are mainly affected by nonzero fourth cumulants and cross-cumulants of the parent population.

Key Words: Large-sample theory • Nonnormality • Robustness • Sample covariance matrix • Sample roots


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