Abstract: | Unbiased linear estimators are considered for the model where ψ(x) is an unknown contamination. It is assumed that |ψ(x)|?φ(6x6) where φ is a convex function. Minimax analogues of Φp-optimality criteria are introduced. It is shown that, under certain (sufficient) conditions, the least squares estimators and corresponding designs are optimal in the class of all unbiased linear estimators and designs. It is also shown that, in the case when least squares estimators with symmetric design do not lead to an optimal solution, the relative efficiency of optimal least squares is not diminishing and has a uniform lower bound. |