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On the asymptotic normality of functions of uniform spacings
Author(s) -
Beirlant J.,
Janssen P.,
Veraverbeke N.
Publication year - 1991
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3315539
Subject(s) - remainder , normality , mathematics , asymptotic distribution , term (time) , simple (philosophy) , moment (physics) , local asymptotic normality , truncation (statistics) , decomposition , mathematical analysis , calculus (dental) , statistics , physics , arithmetic , medicine , estimator , dentistry , classical mechanics , quantum mechanics , ecology , philosophy , epistemology , biology
Abstract A new proof is given for the asymptotic normality of sum functions of spacings, providing an alternative to the method of Le Cam (1958). The result is obtained under an optimal moment condition. The proof is based on a simple decomposition into a leading term, which is asymptotically normal, and a remainder term, which is shown to be negligible.