Central Limit Theorems for Weakly Stationary Sequences

摘要

Analysis of stochastic processes often involves weakly stationary sequences of random variables. The usefulness of central limit theory in inference based upon large samples of independent variables encourages efforts to carry it over to such sequences of dependent variables. The specialization of a theorem of Hoeffding and Robbins to weakly stationary and m-dependent sequences is generalized herein to a wide class of weakly stationary sequences. Various ways of restricting dependence are discussed. Strigent conditions such as strict stationarity and strong mixing are not assumed, so wide applicability is possible. (Author)