Optimal designs for comparing regression curves - dependence within and between groups
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Date
2021
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Abstract
We consider the problem of designing experiments for the comparison of two regression
curves describing the relation between a predictor and a response in two groups,
where the data between and within the group may be dependent. In order to derive effi-
cient designs we use results from stochastic analysis to identify the best linear unbiased
estimator (BLUE) in a corresponding continuous time model. It is demonstrated that
in general simultaneous estimation using the data from both groups yields more precise
results than estimation of the parameters separately in the two groups. Using the BLUE
from simultaneous estimation, we then construct an efficient linear estimator for finite
sample size by minimizing the mean squared error between the optimal solution in the
continuous time model and its discrete approximation with respect to the weights (of the
linear estimator). Finally, the optimal design points are determined by minimizing the
maximal width of a simultaneous confidence band for the difference of the two regression
functions. The advantages of the new approach are illustrated by means of a simulation
study, where it is shown that the use of the optimal designs yields substantially narrower
confidence bands than the application of uniform designs.
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Keywords
optimal design, comparison of curves, Gaussian white noise model, correlated observations