Locally φp-optimal designs for generalized linear models with a single-variable quadratic polynomial predictor

Hsin Ping Wu, John Stufken

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Finding optimal designs for generalized linear models is a challenging problem. Recent research has identified the structure of optimal designs for generalized linear models with single or multiple unrelated explanatory variables that appear as first-order terms in the predictor. We consider generalized linear models with a single-variable quadratic polynomial as the predictor under a popular family of optimality criteria. When the design region is unrestricted, our results establish that optimal designs can be found within a subclass of designs based on a small support with symmetric structure. We show that the same conclusion holds with certain restrictions on the design region, but in other cases a larger subclass may have to be considered. In addition, we derive explicit expressions for some D-optimal designs.

Original languageEnglish (US)
Pages (from-to)365-375
Number of pages11
JournalBiometrika
Volume101
Issue number2
DOIs
StatePublished - Jun 2014

Keywords

  • Generalized linear model
  • Optimal design

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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