A Review of Kernel Density Estimation with Applications to Econometrics

Abstract

Nonparametric density estimation is of great importance when econometricians want to model the probabilistic or stochastic structure of a data set. This comprehensive review summarizes the most important theoretical aspects of kernel density estimation and provides an extensive description of classical and modern data analytic methods to compute the smoothing parameter. Throughout the text, several references can be found to the most up-to-date and cut point research approaches in this area, while econometric data sets are analyzed as examples. Lastly, we present SIZer, a new approach introduced by Chaudhuri and Marron (2000), whose objective is to analyze the visible features representing important underlying structures for different bandwidths.

Keywords

• Nonparametric Density Estimation
• SiZer
• Plug-In Bandwidth Selectors
• Cross- Validation
• Smoothing Parameter