Key points are not available for this paper at this time.
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.
Dennis D. Boos (Sat,) studied this question.