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On the asymptotic distributions of high‐order spacings statistics
Author(s) -
Guttorp P.,
Lockhart R. A.
Publication year - 1989
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 - 10.2307/3315481
Subject(s) - statistic , mathematics , limiting , order statistic , monte carlo method , asymptotic analysis , asymptotic distribution , statistics , goodness of fit , distribution (mathematics) , statistical physics , mathematical analysis , physics , mechanical engineering , estimator , engineering
Abstract Goodness‐of‐fit tests for the uniform distribution based on sums of smooth functions of m ‐spacings are studied. A limiting sum‐of‐weighted‐chi‐squareds approximation is shown to be accurate uniformly in m for the special cases of analogues of Greenwooďs statistic and Moran's statistic. Asymptotic critical points are provided; theory and Monte Carlo studies show they are accurate for all m provided n is moderately large.