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Semiparametric estimation of the high-dimensional elliptical distribution

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  • Liebscher, Eckhard
  • Okhrin, Ostap

Abstract

This paper investigates semiparametric estimation of the multivariate elliptical distribution in case dimensionality increases with the sample size. We prove the almost sure convergence and derive the convergence rates of the estimator, depending on the sample size, dimensionality, and the bandwidth of the kernel. As an important by-product, we show almost sure convergence with the corresponding convergence rates for the sample covariance matrix under the Frobenius norm. An extensive simulation study has supported the theory.

Suggested Citation

  • Liebscher, Eckhard & Okhrin, Ostap, 2023. "Semiparametric estimation of the high-dimensional elliptical distribution," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    • Handle: RePEc:eee:jmvana:v:195:y:2023:i:c:s0047259x22001336
    DOI: 10.1016/j.jmva.2022.105142
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    References listed on IDEAS

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    4. Liebscher, Eckhard, 2005. "A semiparametric density estimator based on elliptical distributions," Journal of Multivariate Analysis, Elsevier, vol. 92(1), pages 205-225, January.
    5. Yata, Kazuyoshi & Aoshima, Makoto, 2012. "Effective PCA for high-dimension, low-sample-size data with noise reduction via geometric representations," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 193-215.
    6. Bodnar, Taras & Gupta, Arjun K. & Parolya, Nestor, 2014. "On the strong convergence of the optimal linear shrinkage estimator for large dimensional covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 215-228.
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