A Note on the Dependence Conditions for Stationary Normal Sequences

Title & Authors
A Note on the Dependence Conditions for Stationary Normal Sequences
Choi, Hyemi;

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 $\small{D(u_n)}$ 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 $\small{D(u_n)}$ condition is shown weaker than Berman's covariance condition. Examples are given where the Berman condition is satisfied but the distributional mixing is not.
Keywords
Berman condition;covariance;extreme value theory;mixing condition;stationary normal sequence;
Language
English
Cited by
1.
A data-adaptive maximum penalized likelihood estimation for the generalized extreme value distribution, Communications for Statistical Applications and Methods, 2017, 24, 5, 493
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