NA样本下含附加信息时M-泛函的经验似然推断  

Empirical Likelihood Technique for M-functionals in the Presence of Auxiliary Information Under Negatively Associated Samples

作　　者：黄玉[1] 秦永松[2] 

机构地区：[1]南宁学院公共教学部,广西南宁530200 [2]广西师范大学数学与统计学院,广西桂林541004

出　　处：《应用数学》2016年第2期340-351,共12页Mathematica Applicata

基　　金：国家自然科学基金(11271088,11361011,11201088);广西科学基金(2013GXNSFAA019004,2013GXNSFAA019007,2013GXNSFBA019001);南宁学院校级项目(2013XJZK10)

摘　　要：本文研究NA样本下不含附加信息和含附加信息时M-泛函的经验似然推断,将分块技术应用到经验似然方法中,证明M-泛函的对数经验似然比统计量的渐近分布为卡方分布,由此构造NA样本下不含附加信息和含附加信息时M-泛函的经验似然置信区间.同时,对一类M-泛函的检验问题,证明含附加信息比不含附加信息时有更高的功效,并给出数值模拟结果.In this paper,we study the empirical likelihood（EL） inference for M-functionals in the case of no auxiliary information and in the presence of auxiliary information under negatively associated（NA）samples.By using the blockwise technique,it is shown that the EL ratio statistics for M-functionals are asymptotically χ~2-type distributed,which are used to construct the EL-based confidence interval for Mfunctionals in the case of no auxiliary information and in the presence of auxiliary information under negatively associated（NA） samples.We also show that,for a class of testing problems for M-functionals,the efficiency of the testing method in the presence of auxiliary information is higher than that in the case of no auxiliary information.Some simulation results are presented.

关 键 词：M-泛函 附加信息 NA样本 分块经验似然 置信区间 

分 类 号：O212.7[理学—概率论与数理统计]