The Annals of Statistics
- Ann. Statist.
- Volume 37, Number 6B (2009), 4088-4103.
A geometric characterization of c-optimal designs for heteroscedastic regression
We consider the common nonlinear regression model where the variance, as well as the mean, is a parametric function of the explanatory variables. The c-optimal design problem is investigated in the case when the parameters of both the mean and the variance function are of interest. A geometric characterization of c-optimal designs in this context is presented, which generalizes the classical result of Elfving [Ann. Math. Statist. 23 (1952) 255–262] for c-optimal designs. As in Elfving’s famous characterization, c-optimal designs can be described as representations of boundary points of a convex set. However, in the case where there appear parameters of interest in the variance, the structure of the Elfving set is different. Roughly speaking, the Elfving set corresponding to a heteroscedastic regression model is the convex hull of a set of ellipsoids induced by the underlying model and indexed by the design space. The c-optimal designs are characterized as representations of the points where the line in direction of the vector c intersects the boundary of the new Elfving set. The theory is illustrated in several examples including pharmacokinetic models with random effects.
Ann. Statist., Volume 37, Number 6B (2009), 4088-4103.
First available in Project Euclid: 23 October 2009
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Primary: 62K05: Optimal designs
Dette, Holger; Holland-Letz, Tim. A geometric characterization of c -optimal designs for heteroscedastic regression. Ann. Statist. 37 (2009), no. 6B, 4088--4103. doi:10.1214/09-AOS708. https://projecteuclid.org/euclid.aos/1256303537