Handling the curse of dimensionality in multivariate kernel density estimation
Jordan Jimmy Crabbe · SHAREOK (University of Oklahoma; Oklahoma State University; Central Oklahoma University) · 2013
Kernel density estimation (KDE) is the most widely-used practical method for accurate nonparametric density estimation. Many works had been done on both the univariate and multivariate cases showing the efficacy, practicality and applicability of this method. 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. Scott and Wand (1991) demonstrated a progressive deterioration of the multivariate kernel density estimation as the dimension p increases by showing that an increase in sample size is required to attain an equivalent amount of accuracy.