ABSTRACT
T.W. Anderson (1963) derived the asymptotic distribution of the eigenvalues and vectors of the covariance matrix of a sample from a Gaussian distribution. Davis (1977) took his basic method and used it to get some results for the non-Gaussian case. The non-Gaussian case is of interest either because one wants to study the sensitivity of methods to deviations from Gaussianity – e.g. Muirhead (1982) – or because one has to deal with other distributions. For example, the distribution of the random vector might be entirely restricted to some manifold embedded in IR q like the surface of the unit sphere or an hyperboloid of rotation; the case of special interest to this writer is the sphere (see Watson (1983c)).
