A Functional Linear Regression for High‐Resolution 3D Faces

ABSTRACT Many scientific disciplines are faced with the challenge of extracting meaningful information from large, complex and highly structured datasets. A significant portion of contemporary statistical research is dedicated to developing tools for handling such data. This paper introduces a functional linear regression model specifically designed for 3D facial shapes, which are viewed as manifolds. We propose a comprehensive framework that includes converting 3D facial data into functional objects, employing a functional principal component analysis method and utilising a function‐on‐scalar regression model. This framework facilitates computation for high‐dimensional data and is employed to investigate how individual traits, such as age and genetic ancestry, impact the diversity of human facial features.