On the normal uniform local domain of attraction for intermediate order statistics

Segers, Johan
(2001) Statistics & Probability Letters — Vol. 53, n° 4, p. 409-413 (2001)

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Abstract
Let X1,X2,… be independent observations from the absolutely continuous distribution function F with quantile function Q. The density of the normalized order statistic Xn-kn + 1:n converges locally uniformly to the standard normal density for any sequence kn with kn→∞ and kn/n→0 if and only if Log (d/dx) Q(1-1/x) is slowly oscillating.
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  • Katholieke Universiteit LeuvenDepartement Wiskunde

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Segers, J. (2001). On the normal uniform local domain of attraction for intermediate order statistics. Statistics & Probability Letters, 53(4), 409-413. https://doi.org/10.1016/S0167-7152(01)00063-3 (Original work published 2001)