Modelling physical activity profiles in COPD patients: a new approach to variable-domain functional regression models

Motivated by the increasingly common technology for collecting data, like cellphones, smartwatches, etc, functional data analysis has been intensively studied in recent decades, and along with it, functional regression models. However, the majority of functional data methods in general and functional regression models, in particular, are based on the fact that the observed datapresent the same domain. When the data have variable domain it needs to be aligned or registered in order to be fitted with the usual modeling techniques adding computational burden. To avoid this, a model that contemplates the variable domain features of the data is needed, but this type of models are scarce and its estimation method presents some limitations. In this article, we propose a new scalar-on-function regression model for variable domain functional data that eludes the need for alignment and a new estimation methodology that we extend to other variable domain regression models.