Discussion Papers in Statistics and Econometrics Seminar of Economic and Social Statistics University of Cologne
نویسنده
چکیده
Suppose that X is a d-dimensional elliptically distributed random vector with dispersion matrix Σ . Many multivariate statistical methods like principal component analysis, canonical correlation analysis, linear discriminant analysis, and multivariate regression require the covariance or dispersion matrix of X only up to a scaling constant. Hence, the present work concentrates on the shape matrix Ω := d/trΣ ·Σ and the asymptotic distributions of different estimators for Ω are derived. The results follow from the theory of random matrices of the radial type. It is shown how to calculate the asymptotic distributions of shape matrix estimators based on asymptotically normal MLor M-estimators. Some examples are presented which include the canonical version of Tyler’s M-estimator T where trT = d .
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Discussion Papers in Statistics and Econometrics Seminar of Economic and Social Statistics University of Cologne
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