Random central limit theorem for associated random variables and the order of approximation

详细信息    查看全文

• 作者：B.L.S. Prakasa Rao^a ; ^{blsprao@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; M. Sreehari^b
• 关键词：Associated sequences ; Random partial sums ; Random central limit theorem ; Berry&ndash ; Esseen type bound
• 刊名：Statistics & Probability Letters
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：111
• 期：Complete
• 页码：1-7
• 全文大小：353 K

文摘

We consider a random number N_n$N_n$ and strictly stationary associated random variables X_k$X_k$ and form random partial sums $S_{N_n}={\sum }_{j=1}^{N_n}{X}_j$ under the assumption that N_n$N_n$ is independent of the sequence {X_r,r≥1}$\{X_r,r\ge 1\}$ for every n≥1$n\ge 1$. Under certain conditions on the random variables X_k$X_k$ and N_n$N_n$, we obtain the limit distribution of the sequence S_Nn$S_{N_n}$ after suitable normalization. We also obtain an estimate of the order of approximation.