Optimal designs for mixed models in experiments based on ordered units

Dibyen Majumdar, John Stufken

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)1090-1107
Number of pages18
JournalAnnals of Statistics
Issue number3
StatePublished - Jun 2008
Externally publishedYes


  • Block designs
  • Orthogonal array of type II
  • Semibalanced arrays
  • Trend effects
  • Universal optimality
  • Variance components

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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