上界型拟合优度检验

数学物理学报 ›› 2010, Vol. 30 ›› Issue (2): 344-357.

上界型拟合优度检验

张军舰^1|2|李国英³

1.广西师范大学数学科学学院|广西桂林 541004|2.北京工业大学应用数理学院|北京 100124|3.中国科学院数学与系统科学研究院|北京 100080

收稿日期:2008-03-11 修回日期:2009-06-30 出版日期:2010-04-25 发布日期:2010-04-25
基金资助:
广西自然科学基金(0832102)、广西师范大学博士基金、国家自然科学基金(10371126; 10661003)资助.

Supremum-type Tests for Goodness-of-fit

ZHANG Jun-Jian^1|2, LI Guo-Ying³

1.College of Mathematical Sciences, Guangxi Normal University, Guangxi Guilin 541004|2.College of Applied Sciences, Beijing University of Technology, Beijing 100124|3.Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080

Received:2008-03-11 Revised:2009-06-30 Online:2010-04-25 Published:2010-04-25
Supported by:
广西自然科学基金(0832102)、广西师范大学博士基金、国家自然科学基金(10371126; 10661003)资助.

摘要/Abstract

摘要：

对简单零假设情况, 构造出一类上界型拟合优度检验. 取不同的参数$\lambda$和不同的权函数, 这类检验不仅包含许多已存在的检验, 如Kolmogorov-Smirov检验, Berk-Jones检验等, 而且还给出一些新的检验. 众所周知, 对不同的问题, ``最优''的检验是不同的, 有必要对这类检验的性质进行讨论. 该文对任意给定的$\lambda$和较一般的权函数q(?), 在较弱的条件下, 导出了相应上界型检验统计量在零假设下的渐近分布, 研究了它们的局部渐近功效; 在若干固定备择假设下, 对该类检验的功效进行了模拟研究. 模拟结果表明, 在不同的备择假设下, 功效较优的检验是不同的, 不存在对所有情况一致最优的检验.

关键词: 广义非参似然比, 上界型检验, 拟合优度, 渐近分布

Abstract:

For goodness of fit tests with simple null hypothesis, a class of supremum-type tests is investigated. Different parameter λ and different weighted function q(t) result in different tests, including the Kolmogorov-Smirnov
test, Berk-Jones test and Reversed Berk-Jones test. It is well known that for different problems, the “best'' tests are different. It is necessary to discuss the tests for all λ and the general q(t). In this paper, the supremum-type tests for all λ and general q(t) are discussed. The asymptotic distributions of these tests under the null and local alternative hypothesis are derived. Simulation results show that for different alternatives, the more powerful tests different, and there does not exist a uniformly powerful test for all the cases.

Key words: Generalized nonparametric likelihood ratio, Supremum-type tests, Goodness of fit, Asymptotic distribution

中图分类号:

62G10

张军舰, 李国英. 上界型拟合优度检验[J]. 数学物理学报, 2010, 30(2): 344-357.

ZHANG Jun-Jian, LI Guo-Ying. Supremum-type Tests for Goodness-of-fit[J]. Acta mathematica scientia,Series A, 2010, 30(2): 344-357.

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