Vogel, Frederike

A collection of functional quantiles offers a comprehensive portrayal of an individual's distinct physical activity patterns, characterizing the distributions of activity at specific time points over a defined duration. However, the potential to present such a collection as a unified, complete activity surface for each individual remains unexplored in current literature. In this paper, we rectify this shortcoming by proposing functional quantile surface estimation (FQSE), a methodology designed to calculate fully parameterized activity surfaces at the participant level. We embed practical and theoretical requirements by imposing constraints that guarantee non-negativity and non-crossing properties in the direction of the quantile order, respectively. We achieve this by employing a dimensionality reduction algorithm that enforces non-negativity throughout and incorporates a parametric spline-based score structure that is monotonic across different quantile levels. We assess the proposed methodology in terms of the precision and stability of the estimated quantile surfaces. Our findings indicate that our estimations are not only more rational but also more accurate compared to alternative approaches.