Self-normalized central limit theorem for sums of weakly dependent random variables

Let {X _n,n1} be a strictly stationary sequence of weakly dependent random variables satisfyingEX _n=,EX _n ² <,Var S _n /n² and the central limit theorem. This paper presents two estimators of ². Their weak and strong consistence as well as their rate of convergence are obtained for -mixing, -mixing and associated sequences.Supported by a NSF grant and a Taft travel grant. Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221-0025.Supported by a Taft Post-doctoral Fellowship at the University of Cincinnati and by the Fok Yingtung Education Foundation of China. Hangzhou University, Hangzhou, Zhejiang, P.R. China and Department of Mathematics, National University of Singapore, Singapore 0511.