Distributional data analysis of accelerometer data from the NHANES database using nonparametric survey regression models

Accelerometers enable an objective measurement of physical activity levels among groups of individuals in free-living environments, providing high-resolution detail about physical activity changes at different time scales. Current approaches used in the literature for analyzing such data typically employ summary measures such as total inactivity time or compositional metrics. However, at the conceptual level, these methods have the potential disadvantage of discarding important information from recorded data when calculating these summaries and metrics since these typically depend on cut-offs related to exercise intensity zones chosen subjectively or even arbitrarily. Furthermore, much of the data collected in these studies follow complex survey designs. Then, using specific estimation strategies adapted to a particular sampling mechanism is mandatory. The aim of this paper is two-fold. First, a new functional representation of a distributional nature accelerometer data is introduced to build a complete individualized profile of each subject's physical activity levels. Second, we extend two nonparametric functional regression models, kernel smoothing and kernel ridge regression, to handle survey data and obtain reliable conclusions about the influence of physical activity in the different analyses performed in the complex sampling design NHANES cohort and so, show representation advantages.