Principal components in the nonnormal case: The test of equality of Q roots

The limiting distribution of the likelihood ratio statistic Wq 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 Wq is not robust to departures from normality and that Wq cannot be used for nonnormal populations with long tails. For the class of elliptical populations the limiting distribution of Wq can be expressed in close form. A corrected test statistic, Wq*, is proposed that can be used in principal component analysis when sampling from elliptical populations.Principal components robustness test for sphericity test for equality of variance elliptical populations nonnormal model

Polysomnographic characteristics of young manic patients. Comparison with unipolar depressed patients and normal control subjects

Although sleep disturbance is a prominent feature of mania, its polysomnographic (PSG) features have received little study. To investigate more systematically the PSG characteristics of sleep in mania, all-night PSG evaluations were performed for two to four consecutive nights in 19 young manic patients (age range, 18 to 36 years), 19 age-matched patients with major depression, and 19 age-matched normal control subjects. Manic and depressed patients displayed nearly identical profiles of PSG abnormalities compared with normal control subjects, including disturbed sleep continuity, increased percentage of stage 1 sleep, shortened rapid eye movement latency, and increased rapid eye movement density. These results are similar to those reported in previous studies of major depression, and they are consistent with the possibility that the sleep disturbance in mania and major depression is caused by the same mechanism