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A semiparametric density estimator based on elliptical distributions


  • Liebscher, Eckhard


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.

Suggested Citation

  • Liebscher, Eckhard, 2005. "A semiparametric density estimator based on elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 92(1), pages 205-225, January.
  • Handle: RePEc:eee:jmvana:v:92:y:2005:i:1:p:205-225

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    References listed on IDEAS

    1. Liebscher E., 1998. "On A Class Of Plug-In Methods Of Bandwidth Selection For Kernel Density Estimators," Statistics & Risk Modeling, De Gruyter, vol. 16(3), pages 229-244, March.
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    Cited by:

    1. Battey, Heather & Linton, Oliver, 2014. "Nonparametric estimation of multivariate elliptic densities via finite mixture sieves," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 43-67.
    2. Eckhard Liebscher & Wolf-Dieter Richter, 2016. "Estimation of Star-Shaped Distributions," Risks, MDPI, Open Access Journal, vol. 4(4), pages 1-37, November.
    3. Hallin, Marc & Paindaveine, Davy, 2009. "Optimal tests for homogeneity of covariance, scale, and shape," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 422-444, March.


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