一类相合的分位点型检验  

A Class of Consistent Quantile-type Tests

作　　者：赵建昕[1] 徐兴忠[2] 

机构地区：[1]海军潜艇学院二系,青岛266071 [2]北京理工大学数学学院,北京100081

出　　处：《应用数学学报》2012年第1期168-188,共21页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(10771015)资助项目

摘　　要：广义非参数似然比检验统计量是一类很广的统计量,包含了众多重要的检验统计量,如Anderson-Darling(AD)等.利用Rubin的随机经验分布函数替代经验分布函数的方法,得到了广义非参数似然比检验统计量的新版本,构造了新的检验统计量.由于新的检验统计量在给定样本下仍然是随机变量,选择了它的分位点和期望作为检验统计量,分别称之为分位点型检验统计量和期望型检验统计量.在简单假设情况下,证明了分位点型检验统计量和期望型检验统计量在固定备择下的相合性.模拟结果显示,在某些备择下,新的检验的功效明显高于原有的基于经验分布函数的检验的功效.Generalized nonparametric likelihood ratio test statistics is a broad class, which contains a number of important test statistics, such as AD, etc. The new version is obtained by substituting the Rubin＇s EDF for the classical EDF in Generalized nonparametric likeli- hood ratio test statistics, new randomized statistics are derived. Since the new statistics are still random for the given sample. The quantile and expectation of the randomized statistics are chosen as test statistics. Under simple hypothesis, the consistency of the above statis- tics under the given alternative hypothesis is proved. Simulation results show that the new method enables substantial improvement of the previous tests against some alternatives.

关 键 词：随机距离 Rubin的随机经验分布函数 拟合优度检验 分位点型检验 期望型检验 

分 类 号：O212.1[理学—概率论与数理统计]