Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (2): 344-357.

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Supremum-type Tests for Goodness-of-fit

ZHANG Jun-Jian1|2, LI Guo-Ying3   

  1. 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.

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

CLC Number: 

  • 62G10
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