## The Annals of Statistics

### Optimal crossover designs for the proportional model

Wei Zheng

#### Abstract

In crossover design experiments, the proportional model, where the carryover effects are proportional to their direct treatment effects, has draw attentions in recent years. We discover that the universally optimal design under the traditional model is E-optimal design under the proportional model. Moreover, we establish equivalence theorems of Kiefer–Wolfowitz’s type for four popular optimality criteria, namely A, D, E and T (trace).

#### Article information

Source
Ann. Statist., Volume 41, Number 4 (2013), 2218-2235.

Dates
First available in Project Euclid: 23 October 2013

https://projecteuclid.org/euclid.aos/1382547519

Digital Object Identifier
doi:10.1214/13-AOS1148

Mathematical Reviews number (MathSciNet)
MR3127864

Zentralblatt MATH identifier
1277.62191

Subjects
Primary: 62K05: Optimal designs
Secondary: 62J05: Linear regression

#### Citation

Zheng, Wei. Optimal crossover designs for the proportional model. Ann. Statist. 41 (2013), no. 4, 2218--2235. doi:10.1214/13-AOS1148. https://projecteuclid.org/euclid.aos/1382547519

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#### Supplemental materials

• Supplementary material: Appendix for optimal crossover designs for the proportional model. This document is to provide a general algorithm to derive optimal $P_{\langle d\rangle}$ for arbitrary values of $\lambda_{0}$ and $\Sigma$ based on the equivalence theorems.