Optimal Experimental Designs for Sparse Functional Data: A Review

Sparse functional data analysis (FDA) is powerful and increasingly popular for extracting insightful information from functional/longitudinal data collected sparsely over a continuous domain. Although numerous methods have been developed for analyzing such data, the effectiveness of resulting inferences depends critically on the experimental design used for data collection. Optimal design theory provides a principled framework for improving estimation accuracy and efficiency through strategically chosen sampling schemes. This review synthesizes the current literature on optimal experimental design in the context of sparse FDA, highlighting recent methodological developments, comparing key design criteria, and discussing practical applications and existing limitations.