Construction D-optimal designs of experiments for linear multiple regression with heteroscedastic observations

Authors

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

Keywords:

multiple regressions, homoscedastic observations, heteroscedastic observations, saturated optimal designs

Abstract

In article the problem of construction exact D-optimal designs of experiments for linear multiple regression in a case when variance of errors of observations depend on a point in which is made is investigated. Class of functions which describe change variance of heteroscedastic observations is defined for which it is possible construct D-optimal continues designs of experiments. For linear multiple regression with three factors it is constructed five different types of D-optimal continues designs of experiments with heteroscedastic observations. For each of these types the own class of functions describing change variance of observations is defined.

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 2 k designs of resolution III, when N ≡ 1 or 2 mod 4. Mathematische Operationsforschung und Statistik Series Statistics. 1983;14(3):367–379. DOI: 10.1080/02331888308801711.
  2. Kirlitsa VP. Exact D-optimal designs of experiments for linear 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 lineal multiple regression with heteroscedastic observations. Journal of the Belarusian State University. Mathematics and Informatics. 2017;3:53–59. Russian.
  5. Ermakov SM, Zhiglyavskii AA. Matematicheskaya teoriya optimal’nogo eksperimenta [The mathematical theory of optimal design]. Moscow: Nauka; 1987. 320 p. Russian.

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Published

2019-07-15

Issue

No. 2 (2019): 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. 2019. Construction D-optimal designs of experiments for linear multiple regression with heteroscedastic observations. Journal of the Belarusian State University. Mathematics and Informatics. 2 (Jul. 2019), 27–33. DOI:https://doi.org/10.33581/2520-6508-2019-2-27-33.