The functional T(F) = ∫ 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(Fₙ) obtained by evaluating T(·) at the sample df Fₙ is seen to be asymptotically normal and to obey a law of the iterated logarithm.
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Dennis D. Boos (1979) studied this question.
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