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 D-s- 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 D-1-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.
Designing to detect heteroscedasticity in a regression model / A. Lanteri, S. Leorato, J. Lopez-Fidalgo, C. Tommasi. - In: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B STATISTICAL METHODOLOGY. - ISSN 1369-7412. - (2023), pp. qkad004.1-qkad004.12. [Epub ahead of print] [10.1093/jrsssb/qkad004]
Designing to detect heteroscedasticity in a regression model
A. Lanteri
Primo
;S. Leorato;C. TommasiUltimo
2023
Abstract
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 D-s- 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 D-1-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.File | Dimensione | Formato | |
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