A semiparametric density estimator based on elliptical distributions

  • Authors:

  • Eckhard Liebscher

  • Affiliations:

  • Institute of Mathematics, Technical University Ilmenau, D-98684 Ilmenau/Thür, Germany

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2005

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Abstract

In the paper we study a semiparametric density estimation method based on the model of an elliptical distribution. The method considered here shows a way to overcome problems arising from the curse of dimensionality. The optimal rate of the uniform strong convergence of the estimator under consideration coincides with the optimal rate for the usual one-dimensional kernel density estimator except in a neighbourhood of the mean. Therefore the optimal rate does not depend on the dimension. Moreover, asymptotic normality of the estimator is proved.