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

Lei He and Daojiang He ()
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Lei He: Anhui Normal University
Daojiang He: Anhui Normal University

Statistical Papers, 2023, vol. 64, issue 6, No 8, 1997-2013

Abstract: 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.

Keywords: Bayesian design; Maximin design; Product designs; Multi-factor models; Heteroscedastic errors; 62K05 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00362-022-01368-y

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