上界型拟合优度检验

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λ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λ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.

Supremum-type Tests for Goodness-of-fit

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-Smirnovtest, 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.