Each week, we select a recently published Open Access article to feature. This week’s article comes from from Stat and develops trend filtering for estimating trend of functional data. 

The article’s abstract is given below, with the full article available to read here.

Wakayama, T., & Sugasawa, S. (2023). Trend filtering for functional data. Stat, 12( 1), e590. https://doi.org/10.1002/sta4.590

Despite increasing accessibility to function data, effective methods for flexibly estimating underlying functional trend are still scarce. We thereby develop a functional version of trend filtering for estimating trend of functional data indexed by time or on general graph by extending the conventional trend filtering, a powerful nonparametric trend estimation technique for scalar data. We formulate the new trend filtering by introducing penalty terms based on L2-norm of the differences of adjacent trend functions. We develop an efficient iteration algorithm for optimizing the objective function obtained by orthonormal basis expansion. Furthermore, we introduce additional penalty terms to eliminate redundant basis functions, which leads to automatic adaptation of the number of basis functions. The tuning parameter in the proposed method is selected via cross validation. We demonstrate the proposed method is locally adaptive and can identify change points through simulation studies and applications to real-world datasets.