D-Optimal Designs for Multivariate Linear and Quadratic Polynomial Regression

Fu-Chuen Chang ； Ya-Huei Chen

《中國統計學報》 42卷4期 (2004/12) Pp. 383-402

https://doi.org/10.29973/JCSA.200412.0004

並列摘要

This paper discusses the approximate and the exact D-optimal design problems for the common multivariate linear and quadratic polynomial regression on some convex design spaces. For the linear polynomial regression, we consider various design spaces including q-simplex, q-ball and convex hull of a set of finite points. It is shown that the approximate and exact D-optimal designs are concentrated on the extreme points of the design space. The structure of the optimal designs on regular polygons or regular polyhedra is also discussed. For the quadratic polynomial regression, the design space considered is a q-ball. The configuration of the approximate and exact optimal designs for quadratic model in two variables on a disk is also investigated.

並列關鍵字

Approximate design ； convex hull ； D-optimal ； exact design ； linear ； polynomial regression ； q-ball ； quadratic ； simplex

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