Marčenko-Pastur law for Tyler's M-estimator
نویسندگان
چکیده
منابع مشابه
Tyler's M-estimator, random matrix theory, and generalized elliptical distributions with applications to finance
In recent publications standard methods of random matrix theory were applied to principal components analysis of high-dimensional financial data. We discuss the fundamental results and potential shortcomings of random matrix theory in the light of the stylized facts of empirical finance. Especially, our arguments are based on the impact of nonlinear dependencies such as tail dependence. After a...
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The traditional class of elliptical distributions is extended to allow for asymmetries. A completely robust dispersion matrix estimator (the ‘spectral estimator’) for the new class of ‘generalized elliptical distributions’ is presented. It is shown that the spectral estimator corresponds to an M-estimator proposed by Tyler (1983) in the context of elliptical distributions. Both the generalizati...
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متن کاملDISCUSSION PAPERS IN STATISTICS AND ECONOMETRICS SEMINAR OF ECONOMIC AND SOCIAL STATISTICS UNIVERSITY OF COLOGNE No. 2/07 Tyler’s M-Estimator, Random Matrix Theory, and Generalized Elliptical Distributions with Applications to Finance
In recent publications standard methods of random matrix theory were applied to principal components analysis of high-dimensional financial data. We discuss the fundamental results and potential shortcomings of random matrix theory in the light of the stylized facts of empirical finance. Especially, our arguments are based on the impact of nonlinear dependencies such as tail dependence. After a...
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We prove that Kendall’s Rank correlation matrix converges to the Marčenko Pastur law, under the assumption that observations are i.i.d random vectors X1, . . . , Xn with components that are independent and absolutely continuous with respect to the Lebesgue measure. This is the first result on the empirical spectral distribution of a multivariate U -statistic.
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عنوان ژورنال:
- J. Multivariate Analysis
دوره 149 شماره
صفحات -
تاریخ انتشار 2016