Weak consistency of least-squares estimators in linear models

Let Yn, n>=1, be a sequence of integrable random variables with EYn = xn1[beta]1 + xn2[beta]2 + ... + xnp[beta]p, where the xij's are known and [beta]T = ([beta]1, [beta]2,..., [beta]p) unknown. Let bn be the least-squares estimator of [beta] based on Y1, Y2,..., Yn. Weak consistency of bn, n>=1, has been considered in the literature under the assumption that each Yn is square integrable. In this paper, we study weak consistency of bn, n>=1, and associated rates of convergence under the minimal assumption that each Yn is integrable.