Moment inequalities for S n under general dependence restrictions, with applications

Abstract

Abstract : Consider a sum composed of a sequence of random variables and a sequence of constants. This paper establishes moment inequalities with dependence restrictions imposed upon the random variables but not depending upon the constants. A further inequality of more complicated form is also established. The dependence restrictions considered are either of the weak multiplicative type or of related types, namely exchangeable sequences and strongly mixing sequences. Three applications are developed. One treats the almost sure convergence of series under mild dependence restrictions and finite limit conditions. Secondly, an improved technique is presented for the problem of establishing the rate of convergence in the central limit theorem for simple linear rank statistics. Finally, the central limit theorem for strongly mixing summands is treated.