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

Authors

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

Keywords:

D-optimal experimental designs, linear multiple regression, heteroscedastic observations

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

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  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.
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Published

2020-07-30

Issue

No. 2 (2020): Journal of the Belarusian State University. Mathematics and Informatics

Section

Probability Theory and Mathematical Statistics

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How to Cite

[1]
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 (Jul. 2020), 59–67. DOI:https://doi.org/10.33581/2520-6508-2020-2-59-67.