Locally D-optimal designs for spline measurement error models with estimated knots

This paper is concerned with the problem of constructing the locally D-optimal designs for spline measurement error models with estimated knots, where the degree of splines is at most m in each subinterval delimited by knots and it is continuous and differentiable at any knot. Given the number of knots in advance, an equivalence theorem is established and used to check the D-optimality of designs. The characterizations of the locally D-optimal designs are provided under certain conditions. It is shown that the support points of the D-optimal designs for such models are associated with the endpoints of the design interval. The locally D-optimal designs for a class of the models can be determined explicitly. Two examples are presented for illustration.