一类统计量的强大数律和重对数律的精确极限性质  

Precise Asymptotic in the Laws of Large Numbers and Law of Iterated Logarithm for Some Statistics

作　　者：周君兴[1] 杨辉煌[1] 陆传荣[1] 

机构地区：[1]浙江财经学院数学与统计学院,杭州310012

出　　处：《数学年刊（A辑）》2006年第6期807-814,共8页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.10471126)浙江省自然科学基金(No.101016)资助的项目.

摘　　要：设{xn,m≥1}是独立同分布随机变量序列,EX1=0,EX12=1．设Tn= Tn(X1,…,Xn)是随机函数且Tn=Sn+Rn．本文证明在E|Rn|2∨r<∞或E|Rn|<∞下,对随机函数Tn成立着Baum-Katz强大数律和重对数律的精确极限性质的一般结果．由此作为推论,对U-统计量,Von-Mises统计量,线性过程,移动平均过程,线性模型中误差方差估计和功率和等在适当矩条件下均可写出Baum-Katz强大数律和重对数律的精确极限性质．Let {Xn,-∞〈 n 〈 ∞} be a sequence of independent identically distributed oo random variables with EX1 = 0, EX^21 = 1 and let Sn=EX^21=1.设Sn=n∑i=1Xi,TnTn（X1,…Xn） be a statistic （or random functions） such that： Tn = Sn ＋ Rn. This paper gives an universal result in precise asymptotic of the Baum-Katz laws of large numbers and the law of iterated logarithms for Tn under some moment condition, such as E｜Rn｜2vr 〈 ∞ or E｜Rn｜] 〈 ∞. As a consequence, it can be shown that the precise asymptotic of the LLN and LIL hold for Ustatistics, Von-Mises statistics, linear processes, moving average processes, error variance estimates in linear models and power sums etc.

关 键 词：统计量 强大数律 重对数律 精确渐近极限性质 

分 类 号：O211[理学—概率论与数理统计]