Statistica Sinica

Fu-Chuen Chang and Bo-Jung Jiang

Abstract:In this paper we investigate -point -optimal designs for th degree polynomial regression with weight function on the interval . We propose an algebraic approach and provide a numerical method for the construction of optimal designs. Thus if is a rational function and the information of whether the optimal support contains the boundary points and is available, the problem of constructing -point -optimal designs can be transformed into a differential equation problem. One is led to a matrix that includes a finite number of auxiliary unknown constants, and the differentiation can be solved from a system of polynomial equations in those constants. Moreover, the -point -optimal interior support points are the zeros of a polynomial whose coefficients can be computed from a linear system.

Key words and phrases:Approximate D-optimal design, differential equation, matrix, minimally-supported, rational function, weighted polynomial regression.