D-OPTIMAL DESIGNS FOR WEIGHTED POLYNOMIAL REGRESSION A FUNCTIONAL-ALGEBRAIC APPROACH

This paper is concerned with the problem of computing the approximate D-optimal design for polynomial regression with weight function !(x) > 0 on the design interval I = (m0 a; m0 + a). It is shown that if ! 0 (x)=!(x) is a rational function on I and a is close to zero, then the problem of constructing D-optimal designs can be transformed into a dieren tial equation problem leading us to a certain matrix including a nite number of auxiliary unknown constants, which can be approximated by a Taylor expansion. We provide a recursive algorithm to compute Taylor expansion of these constants. Moreover, the D-optimal interior support points are the zeros of a polynomial which has coecien ts that can be computed from a linear system.

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