GOODNESS-OF-FIT TEST STATISTICS THAT DOMINATE THE KOLMOGOROV STATISTICS

被引:133
作者
BERK, RH
JONES, DH
机构
[1] Department of Statistics, Rutgers University, New Brunswich, 08903, N.J.
来源
ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE | 1979年 / 47卷 / 01期
关键词
D O I
10.1007/BF00533250
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
Two statistics are proposed for the simple goodness-of-fit problem. These are derived from a general principle for combining dependent test statistics that has been discussed elsewhere by the authors. It is shown that these statistics are relatively optimal in the sense of Bahadur efficiency and consequently, are more efficient than any weighted Kolmogorov statistic at every alternative. A curious pathology occurs: Under certain alternatives, the sequence of statistics has a Bahadur efficacy or exact slope only in the weak sense of convergence in law. © 1979 Springer-Verlag.
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页码:47 / 59
页数:13
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