Original Paper

Computational Statistics

, Volume 28, Issue 4, pp 1853-1880

First online:

Inference for vast dimensional elliptical distributions

  • Yves DominicyAffiliated withECARES, Solvay Brussels School of Economics and Management, Université libre de Bruxelles
  • , Hiroaki OgataAffiliated withSchool of International Liberal Studies, Waseda University
  • , David VeredasAffiliated withECARES, Solvay Brussels School of Economics and Management, Université libre de Bruxelles Email author 

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Abstract

We propose a quantile–based method to estimate the parameters of an elliptical distribution, and a battery of tests for model adequacy. The method is suitable for vast dimensions as the estimators for location and dispersion have closed–form expressions, while estimation of the tail index boils down to univariate optimizations. The tests for model adequacy are for the null hypothesis of correct specification of one or several level contours. A Monte Carlo study to three distributions (Gaussian, Student–t and elliptical stable) for dimensions 20, 200 and 2000 reveals the goodness of the method, both in terms of computational time and finite samples. An empirical application to financial data illustrates the method.

Keywords

Quantiles Elliptical family Simulations Heavy tails