Kernel density estimation for compositional data with zeros via hypersphere mapping

Abstract

Compositional data—measurements of relative proportions among components—arise frequently in fields ranging from chemometrics to bioinformatics. While density estimation of such data provides crucial insights into their underlying patterns and enables comparative analyses across groups, existing nonparametric approaches are limited, particularly in handling zero components that commonly occur in real-world datasets. We propose a novel kernel density estimation (KDE) method for compositional data that naturally accommodates zero components by exploiting the geometric correspondence between simplices and hyperspheres. This connection to spherical KDE allows us to establish theoretical guarantees, including consistency of the estimator. Through extensive simulations and real data analyses, we demonstrate our method's advantages over existing approaches, particularly in scenarios involving zero components.