This article examines the current state of methodological and practical developments for resampling inference techniques in functional data analysis, paying special attention to situations where either the data and/or the parameters being estimated take values in a space of functions. It first provides the basic background and notation before discussing bootstrap results from nonparametric smoothing, taking into account confidence bands in density estimation as well as confidence bands in nonparametric regression and autoregression. It then considers the major results in subsampling and what is known about bootstraps, along with a few recent real-data applications of bootstrapping with functional data. Finally, it highlights possible directions for further research and exploration.
Studying Axon-Astrocyte Functional Interactions by 3D Two-Photon Ca2+ Imaging: A Practical Guide to Experiments and “Big Data” Analysis