Designs which have equal numbers of observations taken over a finite set of uniformly spaced points are most popular in practice. For optimum properties of such exact uniform designs, however, reference is often made to the lack of fit (LOF)-optimality of the corresponding absolutely continuous uniform design which is considered as the asymptotic design for the exact uniform designs. It is shown that LOF-optimality in its original form has no relation to exact uniform designs. Subsequently we give conditions under which an interpretation for exact uniform designs is possible.
Model Check Linear Regression Model Regression Function Design Point Uniform Design
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.
The author thanks an unknown referee for her/his careful reading of the first draft and for her/his suggestions.
Biedermann, S. and Dette, H. (2001). Optimal designs for testing the functional form of a regression via nonparametric estimation techniques. Statistics and Probability Letters52, 215–224.MATHCrossRefMathSciNetGoogle Scholar
Bischoff, W. (2002). The structure of residual partial sums limit processes of linear regression models. Theory of Stochastic Processes8,23–28.MathSciNetGoogle Scholar
Bischoff, W., Miller, F. (2000). Asymptotically optimal tests and optimal designs for testing the mean in regression models with applications to change-point problems. Annals of the Institute of Statistical Mathematics52, 658–679.MATHCrossRefMathSciNetGoogle Scholar