Abstract
This paper considers a linear regression model involving both quantitative and qualitative factors and an m-dimensional response variable y. The main purpose of this paper is to investigate D-optimal designs when the levels of the qualitative factors interact with the levels of the quantitative factors. Under a general covariance structure of the response vector y, here we establish that the determinant of the information matrix of a product design can be separated into two parts corresponding to the two marginal designs. Moreover, it is also proved that D-optimal designs do not depend on the covariance structure if we assume hierarchically ordered system of regression models.
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This paper is supported by the National Natural Science Foundation of China (Nos. 11971318, 11871143) and the Fundamental Research Funds for the Central Universities (No. 2232020D-38)
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Yue, RX., Liu, X. & Chatterjee, K. D-optimal Designs for Multiresponse Linear Models with a Qualitative Factor Under General Covariance Structure. Acta Math. Appl. Sin. Engl. Ser. 39, 878–885 (2023). https://doi.org/10.1007/s10255-023-1089-9
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DOI: https://doi.org/10.1007/s10255-023-1089-9