D-optimal experimental designs for linear multiple regression under heteroscedastic observations

  • Valery P. Kirlitsa Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus
DOI: https://doi.org/10.33581/2520-6508-2020-2-59-67

Abstract

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.

Author Biography

Valery P. Kirlitsa, Belarusian State University, 4 Niezaliežnasci Avenue, Minsk 220030, Belarus

PhD (physics and mathematics), docent; associate professor at the department of mathematical modeling and data analysis, faculty of applied mathematics and computer science

References

  1. Moyssiadis C, Kounias S. Exact D-optimal N observations 2k designs of resolution ΙΙΙ, when N ≏ 1 or 2 mod 4. Series Statistics. 1983;14(3):367–379. DOI: 10.1080/02331888308801711.
  2. Kirlitsa VP. Exact D-optimal designs of experiments for linear model of pair regression. Vestnik BGU. Seriya 1. Fizika. Matematika. Informatika. 2016;2:116–122. Russian.
  3. Kirlitsa VP. Exact D-optimal designs of experiments for linear multiple model with linear variance of observations. In: Computer data analysis and modeling. Robustness and computer intensive methods. Proceedings of the Seventh International conference; 2004 September 6–10; Minsk, Belarus. Volume 1. Minsk: Belarusian State University; 2004. p. 165–167.
  4. Kirlitsa VP. Exact D-optimal designs of experiments for linear multiple regression with heteroscedastic observations. Journal of the Belarusian State University. Mathematics and Informatics. 2017;3:53–59. Russian.
  5. Kirlitsa VP. Construction D-optimal designs of experiments for linear multiple regression with heteroscedastic observations. Journal of the Belarusian State University. Mathematics and Informatics. 2019;2:27–33. Russian.
  6. Ermakov SM, Zhiglyavskii AA. Matematicheskaya teoriya optimal’nogo eksperimenta [The mathematical theory of optimal design]. Moscow: Nauka; 1987. 320 p. Russian.
Published
2020-07-30
Keywords: D-optimal experimental designs, linear multiple regression, heteroscedastic observations
How to Cite
Kirlitsa, V. P. (2020). D-optimal experimental designs for linear multiple regression under heteroscedastic observations. Journal of the Belarusian State University. Mathematics and Informatics, 2, 59-67. https://doi.org/10.33581/2520-6508-2020-2-59-67
Issue
No 2 (2020): Journal of the Belarusian State University. Mathematics and Informatics
Section
Probability Theory and Mathematical Statistics

Copyright (c) 2020 Journal of the Belarusian State University. Mathematics and Informatics

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

The authors who are published in this journal agree to the following:

  1. The authors retain copyright on the work and provide the journal with the right of first publication of the work on condition of license Creative Commons Attribution-NonCommercial. 4.0 International (CC BY-NC 4.0).
  2. The authors retain the right to enter into certain contractual agreements relating to the non-exclusive distribution of the published version of the work (e.g. post it on the institutional repository, publication in the book), with the reference to its original publication in this journal.
  3. The authors have the right to post their work on the Internet (e.g. on the institutional store or personal website) prior to and during the review process, conducted by the journal, as this may lead to a productive discussion and a large number of references to this work. (See The Effect of Open Access.)