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

Authors

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

Keywords:

exact D-optimal designs of experiments, linear multiple regression, homoscedastic, heteroscedastic observations, saturated optimal designs

Abstract

In article the problem of construction of 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. The class functions describing change of variance of heteroscedastic observations is constructed for which exact D-optimal designs coincides with exact D-optimal designs for homoscedastic observations. The saturated D-optimal designs of experiments for linear multiple regression with three factors for heteroscedastic observations are constructed. It is demonstrated that is possible to construct infinite incalculable set of such saturated optimal designs.

Author Biography

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

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

References

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  2. Kirlitsa V. P. Exact D-optimal designs of experiments for linear pair regression. Vestnik BGU. Ser. 1, Fiz. Mat. Inform. 2016. No. 2. P. 116 –122 (in Russ.).
  3. Kirlitsa V. P. Exact D-optimal designs of experiments for linear multiple model with linear variance of observations. Comput. data anal. model. Robust. comput. intensive methods. Minsk, 2004. Vol. 1. P. 165–167.
  4. Ermakov S. M., Zhiglavski A. A. [The mathematical theory of optimal design]. Moscow, 1987 (in Russ.).
  5. Kirlitsa V. P. [About structure of D-optimal saturated designs of experiment]. Vestnik BGU. Ser. 1, Fiz. Mat. Inform. 2013. No. 3. P. 86 – 90 (in Russ.).
  6. Williamson J. Determinants whose elements are 0 and 1. Am. Math. Monthly. 1946. Vol. 53. P. 427 – 434.

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Published

2018-02-14

Issue

No. 3 (2017): 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. 2018. Exact D-optimal designs of experiments for linear multiple regression with heteroscedastic observations. Journal of the Belarusian State University. Mathematics and Informatics. 3 (Feb. 2018), 53–59.