Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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A Note on the Dependence Conditions for Stationary Normal Sequences

  • Choi, Hyemi (Department of Statistics, Chonbuk National University)
  • Received : 2015.08.28
  • Accepted : 2015.10.24
  • Published : 2015.11.30
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Abstract

Extreme value theory concerns the distributional properties of the maximum of a random sample; subsequently, it has been significantly extended to stationary random sequences satisfying weak dependence restrictions. We focus on distributional mixing condition $D(u_n)$ and the Berman condition based on covariance among weak dependence restrictions. The former is assumed for general stationary sequences and the latter for stationary normal processes; however, both imply the same distributional limit of the maximum of the normal process. In this paper $D(u_n)$ condition is shown weaker than Berman's covariance condition. Examples are given where the Berman condition is satisfied but the distributional mixing is not.

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References

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