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Excess of Locally D-optimal Designs and Homothetic Transformations. / Grigoriev, Yu. D. ; Melas, V. B. ; Shpilev, P. V. .

в: Vestnik St. Petersburg University: Mathematics, Том 50, № 4, 17.12.2017, стр. 329-336.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Grigoriev, YD, Melas, VB & Shpilev, PV 2017, 'Excess of Locally D-optimal Designs and Homothetic Transformations', Vestnik St. Petersburg University: Mathematics, Том. 50, № 4, стр. 329-336. <https://link.springer.com/article/10.3103%2FS1063454117040082>

APA

Grigoriev, Y. D., Melas, V. B., & Shpilev, P. V. (2017). Excess of Locally D-optimal Designs and Homothetic Transformations. Vestnik St. Petersburg University: Mathematics, 50(4), 329-336. https://link.springer.com/article/10.3103%2FS1063454117040082

Vancouver

Grigoriev YD, Melas VB, Shpilev PV. Excess of Locally D-optimal Designs and Homothetic Transformations. Vestnik St. Petersburg University: Mathematics. 2017 Дек. 17;50(4):329-336.

Author

Grigoriev, Yu. D. ; Melas, V. B. ; Shpilev, P. V. . / Excess of Locally D-optimal Designs and Homothetic Transformations. в: Vestnik St. Petersburg University: Mathematics. 2017 ; Том 50, № 4. стр. 329-336.

BibTeX

@article{6383d2f09ea445cabcdb18dd211bc647,
title = "Excess of Locally D-optimal Designs and Homothetic Transformations",
abstract = "The paper is devoted to the study of homothety{\textquoteright}s influence on the number of optimal design support points under fixed values of a regression model{\textquoteright}s parameters. The Ayen–Peters two-dimensional nonlinear in parameters model used in analytical chemistry is considered. It is shown that the number of optimal design support points must be greater than or equal to the number of parameters depending on certain conditions. The optimal designs with the minimal number of support points are constructed explicitly. Some numerical methods for constructing designs with greater number of points (we suggest to call them excess designs) are used.",
keywords = "избыточный план, локально D-оптимальные планы, преобразование гомотетии, модель Эйена-Петерса, метод исключения, Excess designs, locally D-optimal designs, homothetic transformation, Ayen–Peters model, elimination method",
author = "Grigoriev, {Yu. D.} and Melas, {V. B.} and Shpilev, {P. V.}",
note = "Grigoriev, Y.D., Melas, V.B. & Shpilev, P.V. Excess of locally D-optimal designs and homothetic transformations. Vestnik St.Petersb. Univ.Math. 50, 329–336 (2017). https://doi.org/10.3103/S1063454117040082",
year = "2017",
month = dec,
day = "17",
language = "English",
volume = "50",
pages = "329--336",
journal = "Vestnik St. Petersburg University: Mathematics",
issn = "1063-4541",
publisher = "Pleiades Publishing",
number = "4",

}

RIS

TY - JOUR

T1 - Excess of Locally D-optimal Designs and Homothetic Transformations

AU - Grigoriev, Yu. D.

AU - Melas, V. B.

AU - Shpilev, P. V.

N1 - Grigoriev, Y.D., Melas, V.B. & Shpilev, P.V. Excess of locally D-optimal designs and homothetic transformations. Vestnik St.Petersb. Univ.Math. 50, 329–336 (2017). https://doi.org/10.3103/S1063454117040082

PY - 2017/12/17

Y1 - 2017/12/17

N2 - The paper is devoted to the study of homothety’s influence on the number of optimal design support points under fixed values of a regression model’s parameters. The Ayen–Peters two-dimensional nonlinear in parameters model used in analytical chemistry is considered. It is shown that the number of optimal design support points must be greater than or equal to the number of parameters depending on certain conditions. The optimal designs with the minimal number of support points are constructed explicitly. Some numerical methods for constructing designs with greater number of points (we suggest to call them excess designs) are used.

AB - The paper is devoted to the study of homothety’s influence on the number of optimal design support points under fixed values of a regression model’s parameters. The Ayen–Peters two-dimensional nonlinear in parameters model used in analytical chemistry is considered. It is shown that the number of optimal design support points must be greater than or equal to the number of parameters depending on certain conditions. The optimal designs with the minimal number of support points are constructed explicitly. Some numerical methods for constructing designs with greater number of points (we suggest to call them excess designs) are used.

KW - избыточный план, локально D-оптимальные планы, преобразование гомотетии, модель Эйена-Петерса, метод исключения

KW - Excess designs

KW - locally D-optimal designs

KW - homothetic transformation

KW - Ayen–Peters model

KW - elimination method

M3 - Article

VL - 50

SP - 329

EP - 336

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 4

ER -

ID: 13941576