The purpose of this paper is to suggest some important directions for further study. The author pointed out: “It can be expected that in the future much more attention will be paid to the elliptically contoured distributions.” In the beginning of the paper the author gives a brief introduction to elliptically contoured distributions, such as density, moments, cumulants and conditional distributions. Then he considers two sampling models. One is that a random sample is from an elliptically contoured distribution, i.e., observations are i.i.d. Another is to consider the matrix of observations to be a spherical matrix distribution in a certain sense.
For the first model he gives the asymptotic distribution of the sample mean and covariance matrix and consequently the asymptotic distribution of a function of sample covariance. The maximum likelihood and robust estimation of parameters is also discussed. For the second model several kinds of spherical matrix distributions are introduced. The maximum likelihood estimation and likelihood ratio criteria are discussed.
For the entire collection see [Zbl 0779.00022].