TY - JOUR

T1 - Excess and saturated D-optimal designs for the rational model

AU - Grigoriev, Yu. D.

AU - Melas , V. B.

AU - Shpilev, P. V.

PY - 2019

Y1 - 2019

N2 - For a rational two-dimensional nonlinear in parameters model used in analytical chemistry, we investigate how homothetic transformations of the design space affect the number of support points in the optimal designs. We show that there exist two types of optimal designs: a saturated design (i.e. a design with the number of support points which is equal to the number of parameters) and an excess design (i.e. a design with the number of support points which is greater than the number of parameters). The optimal saturated designs are constructed explicitly. Numerical methods for constructing optimal excess designs are used.

AB - For a rational two-dimensional nonlinear in parameters model used in analytical chemistry, we investigate how homothetic transformations of the design space affect the number of support points in the optimal designs. We show that there exist two types of optimal designs: a saturated design (i.e. a design with the number of support points which is equal to the number of parameters) and an excess design (i.e. a design with the number of support points which is greater than the number of parameters). The optimal saturated designs are constructed explicitly. Numerical methods for constructing optimal excess designs are used.

KW - Saturated designs

KW - Excess designs

KW - locally D-optimal designs

KW - Homothetic transformation

KW - Rational model

UR - https://link.springer.com/article/10.1007/s00362-019-01140-9#article-info

M3 - Article

JO - Statistical Papers

JF - Statistical Papers

SN - 0932-5026

ER -