Optimal weighting in linear function estimation

Summary Considering a geometrical treatment (Elfving, 1952) of the Schreiber problem of optimum allocation of weights, the problem can be reduced to a pair of dual problems of linear programming (Belayev, 1972). In case the estimated value is a function of the direct independent observations (Belaev, 1976) the optimum weights must be proportional to the partial derivatives of this function with respect to the observations.