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

Abstract Number:

2526 

Submission Type:

Contributed Abstract 

Contributed Abstract Type:

Speed 

Participants:

Changwon Yoon (1), HYUNBIN CHOI (1), Jeongyoun Ahn (1)

Institutions:

(1) Korea Advanced Institute of Science and Technology, Daejeon, Republic of Korea

Co-Author(s):

HYUNBIN CHOI  
Korea Advanced Institute of Science and Technology
Jeongyoun Ahn  
Korea Advanced Institute of Science and Technology

First Author:

Changwon Yoon  
Korea Advanced Institute of Science and Technology

Presenting Author:

Changwon Yoon  
Department of Industrial & Systems Engineering, KAIST

Abstract Text:

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.

Keywords:

Compositional data|Zero components|Kernel density estimation|Spherical KDE| |

Sponsors:

Section on Nonparametric Statistics

Tracks:

Semi or Nonparametric Methods for Data with complex structure

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