Electronic Journal of Statistics

Analytic solutions for D-optimal factorial designs under generalized linear models

Liping Tong, Hans W. Volkmer, and Jie Yang

Full-text: Open access

Abstract

We develop two analytic approaches to solve D-optimal approximate designs under generalized linear models. The first approach provides analytic D-optimal allocations for generalized linear models with two factors, which include as a special case the $2^{2}$ main-effects model considered by Yang, Mandal and Majumdar [19]. The second approach leads to explicit solutions for a class of generalized linear models with more than two factors. With the aid of the analytic solutions, we provide a necessary and sufficient condition under which a D-optimal design with two quantitative factors could be constructed on the boundary points only. It bridges the gap between D-optimal factorial designs and D-optimal designs with continuous factors.

Article information

Source
Electron. J. Statist., Volume 8, Number 1 (2014), 1322-1344.

Dates
First available in Project Euclid: 20 August 2014

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1408540289

Digital Object Identifier
doi:10.1214/14-EJS926

Mathematical Reviews number (MathSciNet)
MR3263124

Zentralblatt MATH identifier
1298.62136

Subjects
Primary: 62K05: Optimal designs
Secondary: 62K15: Factorial designs

Keywords
Analytic solution D-optimal design factorial design generalized linear model Karush-Kuhn-Tucker condition

Citation

Tong, Liping; Volkmer, Hans W.; Yang, Jie. Analytic solutions for D-optimal factorial designs under generalized linear models. Electron. J. Statist. 8 (2014), no. 1, 1322--1344. doi:10.1214/14-EJS926. https://projecteuclid.org/euclid.ejs/1408540289


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