Open Access
Translator Disclaimer
June 2008 Optimal designs for mixed models in experiments based on ordered units
Dibyen Majumdar, John Stufken
Ann. Statist. 36(3): 1090-1107 (June 2008). DOI: 10.1214/07-AOS518


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.


Download Citation

Dibyen Majumdar. John Stufken. "Optimal designs for mixed models in experiments based on ordered units." Ann. Statist. 36 (3) 1090 - 1107, June 2008.


Published: June 2008
First available in Project Euclid: 26 May 2008

zbMATH: 1216.62114
MathSciNet: MR2418650
Digital Object Identifier: 10.1214/07-AOS518

Primary: 62K05
Secondary: 62K10

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

Rights: Copyright © 2008 Institute of Mathematical Statistics


Vol.36 • No. 3 • June 2008
Back to Top