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- W2017791721 abstract "Let $X_1, X_2,ldots$ be independent observations from a distribution with a regularly varying upper tail with index $a$ greater than 2. For each $n geq 1$, let $X_{1,n} leq cdots leq X_{n,n}$ denote the order statistics based on $X_1,ldots, X_n$. Choose any sequence of integers $(k_n)_{ngeq 1}$ such that $1 leq k_n leq n, k_n rightarrow infty$, and $k_n/n rightarrow 0$. It has been recently shown by S. Csorgo and Mason (1986) that the sum of the extreme values $X_{n,n} + cdots + X_{n-k_n,n}$, when properly centered and normalized, converges in distribution to a standard normal random variable. In this paper, we completely characterize such sequences $(k_n)_{ngeq 1}$ for which the corresponding law of the iterated logarithm holds." @default.
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- W2017791721 date "1987-07-01" @default.
- W2017791721 modified "2023-09-24" @default.
- W2017791721 title "A Law of the Iterated Logarithm for Sums of Extreme Values from a Distribution with a Regularly Varying Upper Tail" @default.
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- W2017791721 doi "https://doi.org/10.1214/aop/1176992074" @default.
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