A Review of Kernel Density Estimation with Applications to Econometrics

TL;DR

This paper provides a comprehensive review of kernel density estimation techniques, emphasizing their theoretical foundations, methods for selecting smoothing parameters, and applications in econometrics, including a new approach called SIZer for feature analysis.

Contribution

It offers an extensive synthesis of classical and modern kernel density estimation methods, highlighting recent research and introducing the SIZer approach for analyzing data structures.

Findings

Summarizes key theoretical aspects of kernel density estimation.

Describes methods for choosing optimal smoothing parameters.

Introduces the SIZer approach for feature analysis.

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.