Nonnormal Multivariate Distributions: Inference Based on Elliptically Contoured Distributions

TL;DRAbstract

Abstract : The class of elliptically contoured distributions, which includes multivariate t-distributions and contaminated normal distributions, serves as a useful generalization of the class of normal multivariate distributions. The density, marginal and conditional densities, and moments of an elliptically contoured distribution are related in a simple fashion to those of a normal distribution. The asymptotic normal distributions of the sample mean and covariance matrix are developed and are compared with the asymptotic distributions of the maximum likelihood estimators of the parameters of an elliptically contoured distribution. The class of elliptically contoured distributions serves as a model for evaluating other robust estimators. Many test procedures for normal distributions are easily modified for the elliptically contoured distributions. Further generalizations are discussed.

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