2021/01/14 by Kirsten Schorning, Holger Dette, Schorning, Kirsten +1
Decision Sciences · Mathematics · #Advanced Statistical Methods and Models #Advanced Statistical Process Monitoring #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Optimal Experimental Design Methods #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2101.05654
openalex publication_date 2021/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the problem of designing experiments for the comparison of two\nregression curves describing the relation between a predictor and a response in\ntwo groups, where the data between and within the group may be dependent. In\norder to derive efficient designs we use results from stochastic analysis to\nidentify the best linear unbiased estimator (BLUE) in a corresponding\ncontinuous time model. It is demonstrated that in general simultaneous\nestimation using the data from both groups yields more precise results than\nestimation of the parameters separately in the two groups. Using the BLUE from\nsimultaneous estimation, we then construct an efficient linear estimator for\nfinite sample size by minimizing the mean squared error between the optimal\nsolution in the continuous time model and its discrete approximation with\nrespect to the weights (of the linear estimator). Finally, the optimal design\npoints are determined by minimizing the maximal width of a simultaneous\nconfidence band for the difference of the two regression functions. The\nadvantages of the new approach are illustrated by means of a simulation study,\nwhere it is shown that the use of the optimal designs yields substantially\nnarrower confidence bands than the application of uniform designs.\n