Statistica Sinica

Mong-Na Lo Huang, Fu-Chuen Chang and Weng Kee Wong***

Abstract:D-optimal designs on the intervals [a,b] are determined for the homoscedastic linear model with regression functionf. Motivation, properties and peculiarities of these designs are provided. In particular, the number of support points of the optimal designs for such models depends on the values of^{T}_{k}(x)=(x,...,x^{k})aandb, as well as an ordered eigenvalue of certain matrix. Analytical results are derived for selected values ofaandb, and where they are not available, numerically optimal designs are computed. The technique here can be used to find optimal designs on more general design intervals and extend some known results (for example, Lau (1983)). Under the model considered here lowerD- andG-efficiency bounds of theD-optimal designs for the full polynomial model are included.

Key words and phrases:D- andG-efficiency, information matrix, Jacobi polynomial, Lagrange interpolation polynomial, Sturm-Liouville equation.