Numerical methods of optimal unblased experimental design in a Hilbert space

Abstract

We consider the optimization of a regression experiment with nonparametric specification of the regression function and the design domain. The main focus is on numerical methods of construction and optimization of unbiased procedures. This paper continues the studies of optimization of a conditional regression experiment in which only the values of some linear constrained functionals of an unknown distribution are observable. The theory developed in [i, 2] makes it possible to consider such problems with limited experimental resources and in the presence of systematic error. In this respect, it is a generalization of the classical theory (see, e.g., [3]) and also of experimental design theory in function spaces [4], differing from previous publications on the theory of unbiased experimental design (see, e.g., [5]) by nonparametric specification of the regression function and the design domain. Unlike [i, 2], the main focus here is on numerical methods of construction and optimization of unbiased procedures.