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Bayesian and maximin optimal designs for heteroscedastic multi-factor regression models

Author

Listed:
  • Lei He

    (Anhui Normal University)

  • Daojiang He

    (Anhui Normal University)

Abstract

In this paper we mainly investigate the problem of optimal designs for multi-factor regression models with partially known heteroscedastic structure. The Bayesian $$\varPhi _q$$ Φ q -optimality criterion proposed by Dette and Wong (Ann Stat 24:2108–2127, 1996), which closely resembles Kiefer’s $$\varPhi _k$$ Φ k -class of criteria, and the standardized maximin D-optimal criterion are considered. More precisely, for heteroscedastic Kronecker product models, it is shown that the product designs formed from optimal designs for sub-models with a single factor are optimal under the two robust criteria. For additive models with intercept, however, sufficient conditions are given in order to search for Bayesian $$\varPhi _q$$ Φ q -optimal and standardized maximin D-optimal product designs. Finally, several examples are presented to illustrate the obtained theoretical results.

Suggested Citation

  • Lei He & Daojiang He, 2023. "Bayesian and maximin optimal designs for heteroscedastic multi-factor regression models," Statistical Papers, Springer, vol. 64(6), pages 1997-2013, December.
    • Handle: RePEc:spr:stpapr:v:64:y:2023:i:6:d:10.1007_s00362-022-01368-y
    DOI: 10.1007/s00362-022-01368-y
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