Handling the Curse of Dimensionality in Multivariate Kernel Density Estimation

• Activity Number: 692
• Type: Contributed
• Date/Time: Thursday, August 13, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Jordan Crabbe*
• Keywords: kernel ; density ; estimation ; dimensionality

Abstract

Kernel density estimation (KDE) is the most widely-used practical method for accurate nonparametric density estimation. Despite the fact that multivariate kernel density estimation is an important technique in multivariate data analysis and has a wide range of applications, its performance worsens exponentially with high dimensional data sets, this phenomenon is called "curse of dimensionality", where there is exponential growth in combinatorial optimization as the dimension of the data set increases. This work proposes a new multivariate kernel density estimation approach which is based on the sample means. The method has the characteristic that it works for self-revolving densities or the ellipsoidally symmetric distributions. It also works for spherical distributions since they can be transformed to ellipsoidally symmetric distributions by undergoing an affine transformation. We applied this new method to the probability density function. Our multivariate kernel density estimation approach which is based on the sample means performs better than the regular multivariate kernel density estimation based on the sample data. We also observed that the proposed multivariate kernel den