On the regularization of singular $c$-optimal designs

Rok, strany: 2009, 611 - 626

We consider the design of $c$-optimal experiments for the estimation of a scalar function $h(θ)$ of the parameters $θ$ in a nonlinear regression model. A $c$-optimal design $ξ^*$ may be singular, and we derive conditions ensuring the asymptotic normality of the Least-Squares estimator of $h(θ)$ for a singular design over a finite space. As illustrated by an example, the singular designs for which asymptotic normality holds typically depend on the unknown true value of $θ$, which makes singular $c$-optimal designs of no practical use in nonlinear situations. Some simple alternatives are then suggested for constructing nonsingular designs that approach a $c$-optimal design under some conditions.

ISO 690:

Pronzato, L. 2009. On the regularization of singular $c$-optimal designs. In Mathematica Slovaca, vol. 59, no.5, pp. 611-626. 0139-9918. DOI: https://doi.org/10.2478/s12175-009-0151-2

APA:

Pronzato, L. (2009). On the regularization of singular $c$-optimal designs. Mathematica Slovaca, 59(5), 611-626. 0139-9918. DOI: https://doi.org/10.2478/s12175-009-0151-2