Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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On the second order property of elliptical multivariate regular variation

  • Moosup Kim (Department of Statistics, Keimyung University)
  • Received : 2024.01.14
  • Accepted : 2024.03.14
  • Published : 2024.07.31
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Abstract

Multivariate regular variation is a popular framework of multivariate extreme value analysis. However, a suitable parametric model needs to be introduced for efficient estimation of its spectral measure. In such a view, elliptical distributions have been employed for deriving such models. On the other hand, the second order behavior of multivariate regular variation has to be specified for investigating the property of the estimator. This paper derives such a behavior by imposing a widely adopted second order regular variation condition on the representation of elliptical distributions. As result, the second order variation for the convergence to spectral measure is characterized by a signed measure with a regular varying index. Moreover, it leads to the asymptotic bias of the estimator. For demonstration, multivariate t-distribution is considered.

Keywords

Acknowledgement

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT): Grant No. RS-2023-00243752.

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