Convergence Of The Bootstrap For Dependent Random Variables

This dissertation consists of three chapters, in which we discuss the convergence of NA bootstrap samples.In chapter one, it is shown that stationary negatively associated sequences satisfy the Moving Block Bootstrap Central Limit Theorem with finite second moment, even with bootstrapped norming.In chapter two, we show that NA sequences satisfy the bootstrap Law of Large Numbers if second moment is finite and limsup, where m and n indicate the bootstrap and original sample sizes seperately.In chapter three, we construct an NA sequence by SAS, and check up the convergence efficiency of the bootstrap by simulations.