Summary
Under general regularity assumptions, we characterize the upper and lower almost sure classes of U k, n , where U 1, n ...U n, n are the order statistics of an i.i.d. sample of size n from the uniform distribution on (0, 1), and where k=k n is a non-decreasing integer sequence such that 1≦k =O(log2 n) as n → ∞.
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Deheuvels, P. Strong laws for the k-th order statistic when k≦c log2 n . Probab. Th. Rel. Fields 72, 133–154 (1986). https://doi.org/10.1007/BF00343900
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DOI: https://doi.org/10.1007/BF00343900