The Annals of Statistics

Universally optimal designs for two interference models

Wei Zheng

Full-text: Open access

Abstract

A systematic study is carried out regarding universally optimal designs under the interference model, previously investigated by Kunert and Martin [Ann. Statist. 28 (2000) 1728–1742] and Kunert and Mersmann [J. Statist. Plann. Inference 141 (2011) 1623–1632]. Parallel results are also provided for the undirectional interference model, where the left and right neighbor effects are equal. It is further shown that the efficiency of any design under the latter model is at least its efficiency under the former model. Designs universally optimal for both models are also identified. Most importantly, this paper provides Kushner’s type linear equations system as a necessary and sufficient condition for a design to be universally optimal. This result is novel for models with at least two sets of treatment-related nuisance parameters, which are left and right neighbor effects here. It sheds light on other models in deriving asymmetric optimal or efficient designs.

Article information

Source
Ann. Statist., Volume 43, Number 2 (2015), 501-518.

Dates
First available in Project Euclid: 24 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.aos/1424787426

Digital Object Identifier
doi:10.1214/14-AOS1287

Mathematical Reviews number (MathSciNet)
MR3316188

Zentralblatt MATH identifier
1314.62173

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

Keywords
Approximate design theory interference model linear equations system pseudo symmetric designs universally optimal designs

Citation

Zheng, Wei. Universally optimal designs for two interference models. Ann. Statist. 43 (2015), no. 2, 501--518. doi:10.1214/14-AOS1287. https://projecteuclid.org/euclid.aos/1424787426


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