On normal approximation for φ -mixing and m -dependent random variables

摘要

In this paper, we estimate the difference Eh(Z(n)) - Eh(Y) between the expectations of real finite Lipschitz function h of the sum Z(n) = (X-1 + ctdot; + X-n)/B-n, where B-n(2) = E(X-1 + ctdot; + X-n)(2) > 0, and a standard normal random variable Y, where real centered random variables X-1,X-2, mldr; satisfy the phi-mixing condition, defined between the "past" and " future", or are m-dependent. In particular cases, under the condition sum;(infinity)(r=1)r phi(r)