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The information matrix, skewness tensor and \(\alpha\)-connections for the general multivariate elliptic distribution. (English) Zbl 0691.62049
Summary: Expressions for the entries of the information matrix and skewness tensor of a general multivariate elliptic distribution are obtained. From these the coefficients of the \(\alpha\)-connections are derived. A general expression for the asymptotic efficiency of the sample mean, when appropriate as an estimator of the location parameter, is obtained. The results are illustrated by examples from the multivariate normal, Cauchy and Student’s t-distributions.

62H05 Characterization and structure theory for multivariate probability distributions; copulas
62H12 Estimation in multivariate analysis
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