Optimal designs based on the maximum quasi-likelihood estimator

Gang Shen, Seung Won Hyun, Weng Kee Wong

Research output: Contribution to journalArticle

Abstract

We use optimal design theory and construct locally optimal designs based on the maximum quasi-likelihood estimator (MqLE), which is derived under less stringent conditions than those required for the MLE method. We show that the proposed locally optimal designs are asymptotically as efficient as those based on the MLE when the error distribution is from an exponential family, and they perform just as well or better than optimal designs based on any other asymptotically linear unbiased estimators such as the least square estimator (LSE). In addition, we show current algorithms for finding optimal designs can be directly used to find optimal designs based on the MqLE. As an illustrative application, we construct a variety of locally optimal designs based on the MqLE for the 4-parameter logistic (4PL) model and study their robustness properties to misspecifications in the model using asymptotic relative efficiency. The results suggest that optimal designs based on the MqLE can be easily generated and they are quite robust to mis-specification in the probability distribution of the responses.

Original languageEnglish (US)
Pages (from-to)128-139
Number of pages12
JournalJournal of Statistical Planning and Inference
Volume178
DOIs
StatePublished - Nov 1 2016

Keywords

  • Approximate design
  • Design efficiency
  • Dose-finding study
  • Equivalence theorem
  • Heteroscedasticity
  • Maximum likelihood estimator

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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