Rotation Sampling for Functional Data

In repeated surveys, rotation sampling is a method that replaces a fraction of the sample at each survey occasion. Rotation samples are known to outperform fixed panels for monitoring population global levels. Motivated by recent applications in sensor networks, we extend rotation sampling to functional data (that is, continuous signals). While conventional rotation designs specify the sample before data collection, our approach uses Markov chains to enable adaptive sampling. Considering the mean function of a stratified population, we study the large-sample behavior of the Horvitz-Thompson estimator. In comparison with fixed panels, our rotation method can reduce the mean estimation error by suitably reallocating the sample during replacements. Further, the variance of the estimation error may decrease by orders of magnitude as the replacements increase in frequency and/or intensity. To investigate the benefits of using both current and past data in the estimation, we develop a composite estimator adapted to functional data. In an application to smart electric meter data, our rotation method enjoys nearly optimal performances and outperforms both fixed panels and conventional rotation samples. Although it uses more data, the composite estimator does not significantly improve upon the Horvitz-Thompson estimator.