Asymptotic normality of linear combinations of order statistics with a smooth score function

Authors
Mason, David M.
Citation
M. Mason, David, Asymptotic normality of linear combinations of order statistics with a smooth score function, Annals of statistics , 9(4), 1981, pp. 899-908
Journal title
Annals of statistics → ACNP
ISSN journal
00905364
Volume
9
Issue
4
Year of publication
1981
Pages
899 - 908
Database
ACNP
SICI code
Abstract
Asymptotic normality of linear combinations of order statistics of the form Tn=n−1∑J(i/(n+1))Xin is investigated along with a slightly trimmed version of Tn. Theorem 5 of Stigler (1974) is extended to show asymptotic normality of Tn for a wide class of score functions. In addition, a proof of Theorem 4 of Stigler (1974) is given.