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Designing to detect heteroscedasticity in a regression model

Journal of the Royal Statistical Society. Series B: Statistical Methodology, ISSN: 1467-9868, Vol: 85, Issue: 2, Page: 315-326
2023
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Article Description

We consider the problem of designing experiments to detect the presence of a specified heteroscedastity in Gaussian regression models. We study the relationship of the Ds - and KL-criteria with the noncentrality parameter of the asymptotic chi-squared distribution of a likelihood-based test, for local alternatives. We found that, when the heteroscedastity depends on one parameter, the two criteria coincide asymptotically and that the D1-criterion is proportional to the noncentrality parameter. Differently, when it depends on several parameters, the KL-optimum design converges to the design that maximizes the noncentrality parameter. Our theoretical findings are confirmed through a simulation study.

Bibliographic Details

Alessandro Lanteri; Samantha Leorato; Chiara Tommasi; Jesús López-Fidalgo

Oxford University Press (OUP)

Mathematics; Decision Sciences

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