D-optimal designs of experiments for trigonometric regression on interval with heteroscedastic observations

Authors

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

Keywords:

continuous D-optimal designs of experiments, trigonometric regression, homoscedastic observations, heteroscedastic observations

Abstract

In article the problem of construction continuous (number of observations is not fixed) D-optimal designs of experiments for trigonometric 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 continuous D-optimal designs of experiments. For trigonometric regression with three factors it is constructed continuous D-optimal designs of experiments with different types 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. Ermakov SM, Zhiglyavskii AA. Matematicheskaya teoriya optimal’nogo eksperimenta [The mathematical theory of optimal design]. Moscow: Nauka; 1987. 320 p. Russian.
  2. Fedorov VV. Teoriya optimal’nogo eksperimenta [Optimal experiment theory]. Moscow: Nauka; 1971. 312 p. Russian.
  3. Hoel PG. Minimax designs in two dimensional regression. Annals of Mathematical Statistics. 1965;36(4):1097–1106. DOI: 10.1214/aoms/1177699984.
  4. Dette H, Melas VB. Optimal designs for estimating individual coefficients in Fourier regression models. Annals of Statistics. 2003;31(5):1669–1692. DOI: 10.1214/aos/1065705122.

Downloads

Published

2020-12-08

Issue

No. 3 (2020): Journal of the Belarusian State University. Mathematics and Informatics

Section

Short Communications

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.)

How to Cite

[1]
Kirlitsa, .V.P. 2020. D-optimal designs of experiments for trigonometric regression on interval with heteroscedastic observations. Journal of the Belarusian State University. Mathematics and Informatics. 3 (Dec. 2020), 80–85. DOI:https://doi.org/10.33581/2520-6508-2020-3-80-85.