The Annals of Statistics

Randomization-based models for multitiered experiments: I. A chain of randomizations

R. A. Bailey and C. J. Brien

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Abstract

We derive randomization-based models for experiments with a chain of randomizations. Estimation theory for these models leads to formulae for the estimators of treatment effects, their standard errors and expected mean squares in the analysis of variance. We discuss the practicalities in fitting these models and outline the difficulties that can occur, many of which do not arise in two-tiered experiments.

Article information

Source
Ann. Statist. Volume 44, Number 3 (2016), 1131-1164.

Dates
Received: August 2013
Revised: May 2015
First available in Project Euclid: 11 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.aos/1460381689

Digital Object Identifier
doi:10.1214/15-AOS1400

Mathematical Reviews number (MathSciNet)
MR3485956

Zentralblatt MATH identifier
1338.62028

Subjects
Primary: 62B15: Theory of statistical experiments 62J05: Linear regression
Secondary: 62J10: Analysis of variance and covariance

Keywords
Analysis of variance expected mean square mixed model multiphase experiments multitiered experiments randomization-based model REML structure tier

Citation

Bailey, R. A.; Brien, C. J. Randomization-based models for multitiered experiments: I. A chain of randomizations. Ann. Statist. 44 (2016), no. 3, 1131--1164. doi:10.1214/15-AOS1400. https://projecteuclid.org/euclid.aos/1460381689


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