Functional data analysis for activity profiles from wearable devices
This talk introduces a nonparametric framework for analyzing physiological sensor data collected from wearable devices. The idea is to apply the stochastic process notion of occupation times to construct activity profiles that can be treated as monotonically decreasing functional data.
Whereas raw sensor data typically need to be pre-aligned before standard functional data methods are applicable, activity profiles are automatically aligned because they are indexed by activity level rather than by follow-up time. We introduce a nonparametric likelihood ratio approach that makes efficient use of the activity profiles to provide a simultaneous confidence band for their mean (as a function of activity level), along with an ANOVA type test. These procedures are calibrated using bootstrap resampling. Unlike many nonparametric functional data methods, smoothing techniques are not needed. Accelerometer data from subjects in a U.S. National Health and Nutrition Examination Survey (NHANES) are used to illustrate the approach. The talk is based on joint work with Hsin-wen Chang (Academia Sinica, Taipei).