On necessary and sufficient conditions for the self-normalized central limit theorem In Honor of Professor Chuanrong Lu on His 85th Birthday

查看全文 作　　者：Qiman [1]Shao

机构地区：[1]Department of Statistics, The Chinese University of Hong Kong

出　　处：《Science China Mathematics》索引2018年第61卷第10期,共8页

基　　金：supported by Hong Kong Research Grants Council General Research Fund(Grant Nos.14302515 and 14304917) 摘　　要：Let X_1, X_2,... be a sequence of independent random variables and S_n=sum X_1 from i=1 to n and V_n^2=sum X_1~2 from i=1 to n . When the elements of the sequence are i.i.d., it is known that the self-normalized sum S_n/V_n converges to a standard normal distribution if and only if max1≤i≤n|X_i|/V_n → 0 in probability and the mean of X_1 is zero. In this paper, sufficient conditions for the self-normalized central limit theorem are obtained for general independent random variables. It is also shown that if max1≤i≤n|X_i|/V_n → 0 in probability, then these sufficient conditions are necessary. 关键词：限制定理正常化中央生日平均数随机概率收敛

相关文献

参考文献（10）
引证文献（1）
耦合文献（0）

参考文献(10)

引证文献(1)

互联网出版许可证新出网证(渝)字10号全国400电话 - 免长途话费

On necessary and sufficient conditions for the self-normalized central limit theorem In Honor of Professor Chuanrong Lu on His 85th Birthday

参考文献(10)

引证文献(1)

用户提示