This article is cited in 1 paper

MATHEMATICS

$D$-optimal designs for a two-dimensional polynomial model

P. V. Shpilev

St. Petersburg State University, 7-9, Universitetskaya nab., St. Petersburg, 199034, Russian Federation

Abstract: The influence of an affine transformation of the design space on the number of support points in the $D$-optimal design has been studied for a two-dimensional polynomial regression model. For a full rank model of degree n, a result was obtained that determines the structure of the $D$-optimal plan. It is proven that for a region of design space that is symmetric about zero, the optimal plan is symmetric as well. This result allows for a significant reduction in the dimensionality of the optimization problem and forms the basis of an algorithm developed by the author for finding $D$-optimal plans for models of incomplete rank in nonsymmetric design regions. The D-efficiency of designs concentrated at equidistant points was investigated.

Keywords: multivariate regression models, two-dimensional polynomial regression models, D-optimal designs, D-efficiency.

UDC: 519.24

MSC: 62K05

Received: 25.11.2023
Revised: 06.12.2023
Accepted: 22.02.2024

DOI: 10.21638/spbu01.2024.310