Optimal designs for comparing regression curves: dependence within and between groups (Q2063883)

With this paper the authors continue their work on optimal design for comparing regression models. Whereas in [\textit{H. Dette} and \textit{K. Schorning}, Ann. Stat. 44, No. 3, 1103--1130 (2016; Zbl 1338.62162)] independent samples are assumed, allows [\textit{H. Dette} et al., Comput. Stat. Data Anal. 113, 273--286 (2017; Zbl 1464.62060)] dependencies within the samples. Now, in the present paper, also correlation between the samples is possible. The authors use the strategy from [\textit{H. Dette} et al., Ann. Stat. 45, No. 4, 1579--1608 (2017; Zbl 1421.62085)] and identify the best linear unbiased estimator (BLUE) in a corresponding continuous model. They show that simultaneous estimation (i.e. using the data from both groups) is more precise than estimation seperately in the both groups. Then the authors develop a discrete approximation of the continuous BLUE. Finally, the optimal design points are determined such that the maximum width of the confidence band for the difference of the two regression functions is minimal. A small simulation study shows that the use of optimal designs leads to substantially narrower confidence bands compared with the use of uniform designs.