Abstract
Two theorems on the asymptotic normality of linear combinations of functions of order statistics are given. Theorem 1 requires a "smooth" scoring function but the underlying df need not be continuous even and can also depend on the sample size. Theorem 2 allows general scoring functions but places additional restrictions on the df. Applications included.
Citation
Galen R. Shorack. "Functions of Order Statistics." Ann. Math. Statist. 43 (2) 412 - 427, April, 1972. https://doi.org/10.1214/aoms/1177692622
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