Abstract
We consider extreme value analysis for independent but nonidentically distributed observations. In particular, the observations do not share the same extreme value index. Assuming continuously changing extreme value indices, we provide a nonparametric estimate for the functional extreme value index. Besides estimating the extreme value index locally, we also provide a global estimator for the trend and its joint asymptotic theory. The asymptotic theory for the global estimator can be used for testing a prespecified parametric trend in the extreme value indices. In particular, it can be applied to test whether the extreme value index remains at a constant level across all observations.
Highlights
Extreme value analysis makes statistical inference on the tail region of a distribution function
Classical extreme value analysis assumes that the observations are independent and identically distributed
We aim at dealing with non-iid observations: we consider a continuously changing extreme value index and try to estimate the functional extreme value index accurately
Summary
Extreme value analysis makes statistical inference on the tail region of a distribution function. De Haan, and Zhou (2016) model the tail region of distributions of non-iid observations by considering the quotient between tails of different distributions and a common tail By assuming that such quotients stay positive and finite as one goes further into the tail, the asymptotic constant is called “scedasis.” Within such a framework, the extreme value index remains unchanged across the non-iid observations. De Haan, and Zhou (2016) proposed two tests for the same purpose In all these studies, the main asymptotic result for the constructed tests is under a more restrictive null than having constant extreme value index only. Our study allows for testing the null hypothesis of having a general prespecified trend in the extreme value index beyond the constant function, such as γ (s) = γ0(s) for all s.
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