Abstract
The functional $T(F) = \int F^{-1}(t)J(t) dt$ associated with linear combinations of order statistics is shown to have a Frechet-type differential. As a corollary, the statistic $T(F_n)$ obtained by evaluating $T(\cdot)$ at the sample df $F_n$ is seen to be asymptotically normal and to obey a law of the iterated logarithm.
Citation
Dennis D. Boos. "A Differential for $L$-Statistics." Ann. Statist. 7 (5) 955 - 959, September, 1979. https://doi.org/10.1214/aos/1176344781
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