On Minimally-supported D-optimal Designs for Polynomial Regression with Log-concave Weight Function |
| |
Authors: | Fu-Chuen Chang Hung-Ming Lin |
| |
Affiliation: | (1) Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, 804, Taiwan, ROC |
| |
Abstract: | This paper studies minimally-supported D-optimal designs for polynomial regression model with logarithmically concave (log-concave) weight functions. Many commonly used weight functions in the design literature are log-concave. For example, and exp(−x 2) in Theorem 2.3.2 of Fedorov (Theory of optimal experiments, 1972) are all log-concave. We show that the determinant of information matrix of minimally-supported design is a log-concave function of ordered support points and the D-optimal design is unique. Therefore, the numerically D-optimal designs can be constructed efficiently by cyclic exchange algorithm. |
| |
Keywords: | Approximate D-optimal design Cyclic exchange algorithm Gershgorin Circle Theorem Log-concave Minimally-supported design Weighted polynomial regression |
本文献已被 SpringerLink 等数据库收录! |