Robust estimation of random parameters with incompletely defined uncertainty

Estimation of a random vector x from an observation vector y described by the linear model y = Hx + v, where v is a noise vector, is considered for cases in which the probability distribution for v is not completely specified. The distribution not completely specified is modelled as a convex set which contains all distributions satisfying some partial specification. A minimax approach is used to define a robust estimate x?? of x, and a bound on the mean square error of x?? is given. This generalizes an approach first given by Masreliez and Martin for cases in which the distribution for x is Gaussian. The error bound is calculated for sample cases and compared with that obtained by the best linear unbiased and the conditional mean estimates.