Kernel Density Estimation for Compositional Data with Zeros using Reflection on Sphere

Oregon Convention Center 

Compositional data refers to data holding information of relative proportion of components in each observation. This type of data can be easily found in various fields such as chemometrics and bioinformatics. Estimating the density of compositional data is crucial for gaining insights of the underlying patterns. For example, estimated density can be used for comparison of compositional structure between distinct groups. Despite its significance, there has been little focus on nonparametric density estimation of compositional data. Furthermore, many prior works assume that the compositional data do not contain zeros even though many real-world data indeed contain zero components. In this work, we propose a kernel density estimation (KDE) method for compositional data which can naturally handle zero components. We leverage the topological equivalence between a simplex and the first orthant of a sphere and use reflection of data to entire orthants, establishing a connection with spherical KDE. We investigate asymptotic properties of the suggested KDE method including consistency and compare with existing methods using simulation and real data analysis.

Compositional data

Zero components

Kernel density estimation

Spherical KDE 

Section on Nonparametric Statistics