APPLICATIONS OF CENTRAL LIMIT-THEOREMS OVER ASYMPTOTICALLY MEASURABLESETS - REGRESSION-MODELS

Consider a regression model X-n = phi(xi(n),Y-n), n is an element of Z (d), and assume that X-n is centered, phi is regular, xi and Y are ind ependent random fields, and that the Central Limit Theorem (CLT) holds for phi(xi; y), for each y fixed, but that Y satisfies only the Stron g Law of Large Numbers applied to (Y-.,Y.-n), for any n is an element of Z(d). Then the CLT holds for X. The basic technique is the applicat ion of the CLT over asymptotically measurable sets.