Designs for estimating an extremal point of quadratic regression models in a hyperball

This paper is devoted to studying optimal designs for estimating an extremal point of a multivariate quadratic regression model in the unit hyperball. The problem of estimating an extremal point is reduced to that of estimating certain parameters of a corresponding nonlinear (in parameters) regression model. For this reduced problem truncated locally D-optimal designs are found in an explicit form. The result is a generalization of the results of Fedorov and Müller for one dimensional quadratic regression function in the unit segment.