Optimality of balanced uniform repeated measurements designs
type: Item
instance of: scholarly article
title: Optimality of balanced uniform repeated measurements designs
zbMATH Open document ID: 0544.62068
author: Joachim Kunert
published in: The Annals of Statistics
publication date: 1984-01-01T00:00:00Z
review text: The experiment of a repeated measurements design is based on n experimental units, t treatments and p periods and is denoted by \(\Omega_{t,n,p}\). It is shown that: i) If \(t=n=p\neq 2\) and if a balanced Latin square exists, this is universally optimal for the estimation of direct effects over \(\Omega_{t,t,t}\). ii) A balanced uniform design is universally optimal for the estimation of direct effects over \(\Omega_{t,2t,t}\) for \(t\geq 6.\) iii) If \(t=n=p\) and a design with given properties exists, then no balanced Latin square design can be universally optimal for the estimation of residual effects. Such an example is presented. iv) If \(n=t(t-1)\) an orthogonal residual effects design is universally optimal for the estimation of residual effects over \(\Omega_{t,n,t}\).
Mathematics Subject Classification ID: 62K05
Mathematics Subject Classification ID: 62K10
Mathematics Subject Classification ID: 62P10
zbMATH DE Number: 3866415
zbMATH Keywords: linear model
zbMATH Keywords: universal optimality
zbMATH Keywords: projection matrix
zbMATH Keywords: generalized inverse
zbMATH Keywords: repeated measurements design
zbMATH Keywords: balanced Latin square
zbMATH Keywords: estimation of direct effects
zbMATH Keywords: balanced uniform design
zbMATH Keywords: orthogonal residual effects design
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176346717
OpenAlex ID: W2060572273
DOI: 10.1214/AOS/1176346717
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description: scientific article; zbMATH DE number 3866415