The Annals of Statistics

Optimal designs for the proportional interference model

Kang Li, Wei Zheng, and Mingyao Ai

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Abstract

The interference model has been widely used and studied in block experiments where the treatment for a particular plot has effects on its neighbor plots. In this paper, we study optimal circular designs for the proportional interference model, in which the neighbor effects of a treatment are proportional to its direct effect. Kiefer’s equivalence theorems for estimating both the direct and total treatment effects are developed with respect to the criteria of A, D, E and T. Parallel studies are carried out for the undirectional model, where the neighbor effects do not depend on whether they are from the left or right. Moreover, the connection between optimal designs for the directional and undiretional models is built. Importantly, one can easily develop a computer program for finding optimal designs based on these theorems.

Article information

Source
Ann. Statist., Volume 43, Number 4 (2015), 1596-1616.

Dates
Received: October 2014
Revised: January 2015
First available in Project Euclid: 17 June 2015

Permanent link to this document
https://projecteuclid.org/euclid.aos/1434546216

Digital Object Identifier
doi:10.1214/15-AOS1317

Mathematical Reviews number (MathSciNet)
MR3357872

Zentralblatt MATH identifier
1331.62383

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

Keywords
Approximate design theory equivalence theorem interference model optimal design proportional model

Citation

Li, Kang; Zheng, Wei; Ai, Mingyao. Optimal designs for the proportional interference model. Ann. Statist. 43 (2015), no. 4, 1596--1616. doi:10.1214/15-AOS1317. https://projecteuclid.org/euclid.aos/1434546216


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