D-Optimal Designs for a Two-Dimensional Polynomial Model

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D-Optimal Designs for a Two-Dimensional Polynomial Model. / Shpilev, P.V.

In: Vestnik St. Petersburg University: Mathematics, Vol. 57, No. 3, 01.09.2024, p. 368-376.

Research output: Contribution to journal › Article › peer-review

Author

Shpilev, P.V. / D-Optimal Designs for a Two-Dimensional Polynomial Model. In: Vestnik St. Petersburg University: Mathematics. 2024 ; Vol. 57, No. 3. pp. 368-376.

BibTeX

@article{7362cb79efc041b3816454f9663695db,

title = "D-Optimal Designs for a Two-Dimensional Polynomial Model",

abstract = "Abstract: The influence of an affine transformation of the design space on the number of support points in a D-optimal design is studied for a two-dimensional polynomial regression model. For a full-rank model of n degree, a result is obtained that determines the structure of the D-optimal design. It is proven that for a region of design space that is symmetric about zero, the optimal design is symmetric as well. This result significantly reduces the dimensionality of the optimization problem and forms the basis of an algorithm developed by me for finding D-optimal designs for rank-deficient models in nonsymmetric design regions. The D efficiency of designs concentrated at equidistant points is investigated. {\textcopyright} Pleiades Publishing, Ltd. 2024. ISSN 1063-4541, Vestnik St. Petersburg University, Mathematics, 2024, Vol. 57, No. 3, pp. 368–376. Pleiades Publishing, Ltd., 2024. Russian Text The Author(s), 2024, published in Vestnik Sankt-Peterburgskogo Universiteta: Matematika, Mekhanika, Astronomiya, 2024, Vol. 11, No. 3, pp. 537–548.",

keywords = "D efficiency, D-optimal designs, multivariate regression models, two-dimensional polynomial regression models",

author = "P.V. Shpilev",

note = "Export Date: 21 October 2024 Адрес для корреспонденции: Shpilev, P.V.; St. Petersburg State UniversityRussian Federation; эл. почта: p.shpilev@spbu.ru Сведения о финансировании: Russian Science Foundation, RSF Сведения о финансировании: 23-21-10013 Текст о финансировании 1: The research was carried out at the expense of a joint grant from the Russian Science Foundation and St. Petersburg Science Foundation no. 23-21-10013, https://rscf.ru/project/23-21-10013/ .",

year = "2024",

month = sep,

day = "1",

doi = "10.1134/s1063454124700225",

language = "Английский",

volume = "57",

pages = "368--376",

journal = "Vestnik St. Petersburg University: Mathematics",

issn = "1063-4541",

publisher = "Pleiades Publishing",

number = "3",

}

RIS

TY - JOUR

T1 - D-Optimal Designs for a Two-Dimensional Polynomial Model

AU - Shpilev, P.V.

N1 - Export Date: 21 October 2024 Адрес для корреспонденции: Shpilev, P.V.; St. Petersburg State UniversityRussian Federation; эл. почта: p.shpilev@spbu.ru Сведения о финансировании: Russian Science Foundation, RSF Сведения о финансировании: 23-21-10013 Текст о финансировании 1: The research was carried out at the expense of a joint grant from the Russian Science Foundation and St. Petersburg Science Foundation no. 23-21-10013, https://rscf.ru/project/23-21-10013/ .

PY - 2024/9/1

Y1 - 2024/9/1

N2 - Abstract: The influence of an affine transformation of the design space on the number of support points in a D-optimal design is studied for a two-dimensional polynomial regression model. For a full-rank model of n degree, a result is obtained that determines the structure of the D-optimal design. It is proven that for a region of design space that is symmetric about zero, the optimal design is symmetric as well. This result significantly reduces the dimensionality of the optimization problem and forms the basis of an algorithm developed by me for finding D-optimal designs for rank-deficient models in nonsymmetric design regions. The D efficiency of designs concentrated at equidistant points is investigated. © Pleiades Publishing, Ltd. 2024. ISSN 1063-4541, Vestnik St. Petersburg University, Mathematics, 2024, Vol. 57, No. 3, pp. 368–376. Pleiades Publishing, Ltd., 2024. Russian Text The Author(s), 2024, published in Vestnik Sankt-Peterburgskogo Universiteta: Matematika, Mekhanika, Astronomiya, 2024, Vol. 11, No. 3, pp. 537–548.

AB - Abstract: The influence of an affine transformation of the design space on the number of support points in a D-optimal design is studied for a two-dimensional polynomial regression model. For a full-rank model of n degree, a result is obtained that determines the structure of the D-optimal design. It is proven that for a region of design space that is symmetric about zero, the optimal design is symmetric as well. This result significantly reduces the dimensionality of the optimization problem and forms the basis of an algorithm developed by me for finding D-optimal designs for rank-deficient models in nonsymmetric design regions. The D efficiency of designs concentrated at equidistant points is investigated. © Pleiades Publishing, Ltd. 2024. ISSN 1063-4541, Vestnik St. Petersburg University, Mathematics, 2024, Vol. 57, No. 3, pp. 368–376. Pleiades Publishing, Ltd., 2024. Russian Text The Author(s), 2024, published in Vestnik Sankt-Peterburgskogo Universiteta: Matematika, Mekhanika, Astronomiya, 2024, Vol. 11, No. 3, pp. 537–548.

KW - D efficiency

KW - D-optimal designs

KW - multivariate regression models

KW - two-dimensional polynomial regression models

UR - https://www.mendeley.com/catalogue/7271f390-3c65-327b-977b-88b6bc900c5b/

U2 - 10.1134/s1063454124700225

DO - 10.1134/s1063454124700225

M3 - статья

VL - 57

SP - 368

EP - 376

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 3

ER -

ID: 126219862