Asymptotic distributions of non-central studentized statistics  

作　　者：SHAO QiMan ZHANG RongMao 

机构地区：[1]Department of Mathematics,Hong Kong University of Science and Technology,Clear Water Bay,Kowloon,Hong Kong [2]Department of Mathematics,Zhejiang University,Hangzhou 310027,China

出　　处：《Science China Mathematics》2009年第6期1262-1284,共23页中国科学：数学（英文版）

基　　金：supported in part by Hong Kong UST (Grant No. DAG05/06.SC);Hong Kong RGC CERG(Grant No. 602206);supported by National Natural Science Foundation (Grant No.10801118);the PhD Programs Foundation of the Ministry of Education of China (Grant No. 200803351094)

摘　　要：Let X 1, ..., X n be independent and identically distributed random variables and W n = W n (X 1, ..., X n ) be an estimator of parameter ?. Denote T n = (W n ? ? 0)/s n , where s n 2 is a variance estimator of W n . In this paper a general result on the limiting distributions of the non-central studentized statistic T n is given. Especially, when s n 2 is the jacknife estimate of variance, it is shown that the limit could be normal, a weighted χ 2 distribution, a stable distribution, or a mixture of normal and stable distribution. Applications to the power of the studentized U- and L- tests are also discussed.Let X1,...,Xn be independent and identically distributed random variables and Wn = Wn(X1,...,Xn) be an estimator of parameter θ.Denote Tn =(Wn - θ0)/sn,where sn2 is a variance estimator of Wn.In this paper a general result on the limiting distributions of the non-central studen-tized statistic Tn is given.Especially,when s2n is the jacknife estimate of variance,it is shown that the limit could be normal,a weighted χ2 distribution,a stable distribution,or a mixture of normal and stable distribution.Applications to the power of the studentized U-and L-tests are also discussed.

关 键 词：non-central studentized statistics studentized U-statistics studentized L-statistics limiting distributions power of tests 62E20 62F05 60F05 

分 类 号：O212[理学—概率论与数理统计]