*D-optimal approximative design of experiment for a cubic regression model on cube*

**doc. Mgr. Radoslav Harman, PhD.****doc. Mgr. Lenka Filová, PhD.****Mgr. Samuel Rosa, PhD.****prof. RNDr. Andrej Pázman, DrSc.****doc. RNDr. Mária Trnovská, PhD.****Mgr. Eva Benková****Ing. Assa Camara****Mgr. Pál Somogyi**

Optimal design of experiments is a discipline of mathematical statistics that deals with methods of planning of an experiment in order to obtain as much information as possible within specified constraints on available resources, or to ensure the required data quality at the lowest possible cost. The results of the research in this discipline are applicable in empirical sciences, medicine, industry, agriculture, but also, e.g., in population surveys. The founder of the school of optimal design of experiments at FMPI is prof. RNDr. Andrej Pázman, DrSc., who is also one of the leading figures in this field of research from the global perspective.

**Selected papers**

- R Harman, A Bachratá, L Filová, Construction of efficient experimental designs under multiple resource constraints,
*Applied Stochastic Models in Business and Industry*32 (1), 2016, pp. 3-17. - S Rosa, R Harman, Optimal approximate designs for comparison with control in dose-escalation studies,
*TEST*26 (3), 2017, pp. 638-660. - Harman R, Trnovská M (2009): Approximate D-optimal designs of experiments on the convex hull of a finite set of information matrices,
*Mathematica Slovaca*59, pp. 693–704. - Pronzato L, Pázman A (2013):
*Design of Experiments in Nonlinear Models*, Springer, New York. - Harman R, Filová L (2014): Computing efficient exact designs of experiments using integer quadratic programming,
*Computational Statistics & Data Analysis*71, pp. 1159–1167. - Pázman A, Pronzato L (2014): Optimum designs accounting for the global nonlinear behavior of the model.
*The Annals of Statistics*42, pp. 194-219. - Sagnol G, Harman R (2015) Computing exact D-optimal designs by mixed integer second-order cone programming,
*Annals of Statistics*43, pp. 2198-2224.