Design optimal sampling plans for functional regression models

Functional regression models are widely considered in practice. To make a precise statistical inference, a good sampling schedule for collecting informative functional data is needed. However, there has not been much research on the optimal sampling schedule design for functional regression model so far. To address this design issue, an efficient computational approach is proposed for generating the best sampling plan in the function-on-function linear regression setting. The obtained sampling plan allows a precise estimation of the predictor function and a precise prediction of the response function. The proposed approach can also be applied to identify the optimal sampling plan for the problem with scalar-on-function linear regression model. Through case studies, this approach is demonstrated to outperform the methods proposed in the previous studies.