The Annals of Statistics

Optimal designs for mixed models in experiments based on ordered units

Dibyen Majumdar and John Stufken

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We consider experiments for comparing treatments using units that are ordered linearly over time or space within blocks. In addition to the block effect, we assume that a trend effect influences the response. The latter is modeled as a smooth component plus a random term that captures departures from the smooth trend. The model is flexible enough to cover a variety of situations; for instance, most of the effects may be either random or fixed. The information matrix for a design will be a function of several variance parameters. While data will shed light on the values of these parameters, at the design stage, they are unlikely to be known, so we suggest a maximin approach, in which a minimal information matrix is maximized. We derive maximin universally optimal designs and study their robustness. These designs are based on semibalanced arrays. Special cases correspond to results available in the literature.

Article information

Ann. Statist., Volume 36, Number 3 (2008), 1090-1107.

First available in Project Euclid: 26 May 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62K05: Optimal designs
Secondary: 62K10: Block designs

Trend effects variance components block designs orthogonal array of type II semibalanced arrays universal optimality


Majumdar, Dibyen; Stufken, John. Optimal designs for mixed models in experiments based on ordered units. Ann. Statist. 36 (2008), no. 3, 1090--1107. doi:10.1214/07-AOS518.

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