Abstract
We extend extreme value statistics to independent data with possibly very
different distributions. In particular, we present novel asymptotic normality
results for the Hill estimator, which now estimates the extreme value index
of the average distribution. Due to the heterogeneity, the asymptotic variance
can be substantially smaller than that in the i.i.d. case. As a special case, we
consider a heterogeneous scales model where the asymptotic variance can be
calculated explicitly. The primary tool for the proofs is the functional central limit theorem for a weighted tail empirical process. A simulation study shows the good finite-sample behavior of our limit theorems. We also present applications to assess the tail heaviness of earthquake energies and of cross-sectional stock market losses.
different distributions. In particular, we present novel asymptotic normality
results for the Hill estimator, which now estimates the extreme value index
of the average distribution. Due to the heterogeneity, the asymptotic variance
can be substantially smaller than that in the i.i.d. case. As a special case, we
consider a heterogeneous scales model where the asymptotic variance can be
calculated explicitly. The primary tool for the proofs is the functional central limit theorem for a weighted tail empirical process. A simulation study shows the good finite-sample behavior of our limit theorems. We also present applications to assess the tail heaviness of earthquake energies and of cross-sectional stock market losses.
Original language | English |
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Place of Publication | Tilburg |
Publisher | CentER, Center for Economic Research |
Pages | 1-26 |
Publication status | Published - 4 Aug 2022 |
Publication series
Name | CentER Discussion Paper |
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Volume | 2022-017 |