Asymptotic distributions for weighted power sums of extreme values
Let X1,n ≤ · · · ≤ Xn,n be the order statistics of n independent random variables with a common distribution function F having right heavy tail with tail index γ. Given known constants di,n, 1 ≤ i ≤ n, consider the weighted power sums Pkn i=1 dn+1−i,n logp Xn+1−i,n, where p > 0 and the kn are pos...
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| Format: | Article |
| Published: |
2021
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| Series: | Acta scientiarum mathematicarum
87 No. 1-2 |
| Kulcsszavak: | Matematika |
| doi: | 10.14232/actasm-020-323-9 |
| Online Access: | http://acta.bibl.u-szeged.hu/73932 |
| Summary: | Let X1,n ≤ · · · ≤ Xn,n be the order statistics of n independent random variables with a common distribution function F having right heavy tail with tail index γ. Given known constants di,n, 1 ≤ i ≤ n, consider the weighted power sums Pkn i=1 dn+1−i,n logp Xn+1−i,n, where p > 0 and the kn are positive integers such that kn → ∞ and kn/n → 0 as n → ∞. Under some constraints on the weights di,n, we prove asymptotic normality for the power sums over the whole heavy-tail model. We apply the obtained result to construct a new class of estimators for the parameter γ. |
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| Physical Description: | 331-346 |
| ISSN: | 2064-8316 |