Statistical variant of the CLT for associated random fields

The asymptotic normality of sums taken over the “regulary”growing subsets of $\mathbf Z^{d}$ is studied for a strictly stationary associated random field $\{X_{j},\,j\in\mathbf Z^{d}\}$, $d\geq1$. In this connection families of random normalizations are introduced which permits us to construct approximate confidence intervals for the unknown mean of the field. These normalizations include the two statistics proposed for processes (i.e. $d=1$) in a recent paper by M. Peligrad and Q.-M. Shao.