Abstract
The limiting distribution of the likelihood ratio statistic W q for testing the hypothesis of equality of q characteristic roots of a covariance matrix is studied in the case of nonnormal populations. It is shown, both theoretically and empirically, that the limiting distribution of W q is not robust to departures from normality and that W q cannot be used for nonnormal populations with long tails. For the class of elliptical populations the limiting distribution of W q can be expressed in close form. A corrected test statistic, W q ∗ , is proposed that can be used in principal component analysis when sampling from elliptical populations.
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