A functional Beta distribution model for time correlated continuous monitoring glucose curves

N. Acar Denizli, P. Delicado

In the context of functional data from wearable devices, we study continuous glucose curves as a function of time. A particular feature of these curves is their high degree of smoothness. We argue that the observed smoothness is a consequence of two different reasons. On the one hand, the expected value of the glucose curves changes smoothly with time. On the other hand, successive observations of the glucose level are highly correlated. The functional models we found in the literature usually consider the first aspect, but rarely the second (dependence between observations at different times). This deficiency is particularly evident for generalized functional models. We present a functional Beta distribution model with correlated time observations for modeling continuous glucose monitoring curves. This model can be estimated by local maximum likelihood when there are repeated measures (each subject was followed for several days). We illustrate our proposal with the REPLACE-BG dataset.

Keywords: Beta distribution, nonparametric smoothing, wearable device data

Functional data analysis I
June 10, 2025  11:30 AM
MR 1

L. González de la Fuente, A. Nieto Reyes, P. N. Terán Agraz

E. Jerez López, J. R. Berrendero Díaz, J. L. Torrecilla Noguerales

A. Suárez, J. L. Torrecilla, C. Ramos-Carreño, J. R. Berrendero, A. Muñoz-Perera