Geodesic
$D$-optimal experimental designs for linear multiple regression under heteroscedastic observations
Journal of the Belarusian State University. Mathematics and Informatics, Tome 2 (2020), pp. 59-67.

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The problem of construction of «continuous» (number of observations is not fixed) and «exact» (number of observations is fixed) $D$-optimal experimental designs for linear multiple regression in the case when variance of errors of observations depends on regressor value is studied in this paper. Families of functions that determine heteroscedastic observations are found for which it is possible to construct «continuous» and «exact» $D$-optimal experimental designs. «Continuous» $D$-optimal experimental designs under four different types of heteroscedasticity are constructed for linear multiple regression with three regressors.
Keywords: $D$-optimal experimental designs; linear multiple regression; heteroscedastic observations. 
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V. P. Kirlitsa. $D$-optimal experimental designs for linear multiple regression under heteroscedastic observations. Journal of the Belarusian State University. Mathematics and Informatics, Tome 2 (2020), pp. 59-67. http://geodesic.mathdoc.fr/item/BGUMI_2020_2_a4/

[1] C. Moyssiadis, S. Kounias, “Exact D-optimal N observations 2 (in exp. k) designs of resolution III, when N-1 or 2 mod 4”, Series Statistics, 14(3) (1983), 367–379 | DOI | MR | Zbl

[2] V. P. Kirlitsa, “Tochnye D-optimalnye plany eksperimentov dlya lineinoi modeli parnoi regressii”, Vestnik BGU. Fizika. Matematika. Informatika, 2 (2016), 116–122

[3] V. P. Kirlitsa, “Exact D-optimal designs of experiments for linear multiple model with linear variance of observations”, Computer data analysis and modeling. Robustness and computer intensive methods. Proceedings of the Seventh International conference (Belarus), 2004, 165–167, Minsk: Belarusian State University

[4] V. P. Kirlitsa, “Tochnye D-optimalnye plany eksperimentov dlya lineinoi mnozhestvennoi regressii s neravnotochnymi nablyudeniyami”, Zhurnal Belorusskogo gosudarstvennogo universiteta. Matematika. Informatika, 3 (2017), 53–59 | MR

[5] V. P. Kirlitsa, “Postroenie D-optimalnykh planov eksperimentov dlya lineinoi mnozhestvennoi regressii s neravnotochnymi nablyudeniyami”, Zhurnal Belorusskogo gosudarstvennogo universiteta. Matematika. Informatika, 2 (2019), 27–33 | MR | Zbl

[6] S. M. Ermakov, A. A. Zhiglyavskii, “Matematicheskaya teoriya optimalnogo eksperimenta”, Moskva: Nauka, 1987, 320