In a linear model Y = X[beta] + Z a linear functional [beta] -- [gamma]'[beta] is to be estimated under squared error loss. It is well known that, provided Y is normally distributed, the ordinary least squares estimation function minimizes the risk uniformly in the class of all equivariant...

The weak convergence of certain functionals of a sequence of stochastic processes is investigated. The functionals under consideration are of the form f[phi](x) = [integral operator] [phi] (t, x(t))[mu](dt). The main result is as follows: If a sequence is weakly tight in a certain sense, and, in...