  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.
