A tutorial on kernel density estimation and recent advances. Issue 1 (1st January 2017)

• Record Type: Journal Article
• Authors: Chen, Yen-Chi
• Is Part Of: Biostatistics & epidemiology. Volume 1:Issue 1(2017)
• Page Start: 161
• Page End: 187
• Publication Date: 2017-01-01
• Subjects: Kernel density estimation -- nonparametric statistics -- confidence bands -- bootstrap; Epidemiology -- Periodicals; Biometry -- Periodicals; 614.42
• DOI: 10.1080/24709360.2017.1396742
• Languages: English
• ISSNs: 2470-9360

Abstract

ABSTRACT: This tutorial provides a gentle introduction to kernel density estimation (KDE) and recent advances regarding confidence bands and geometric/topological features. We begin with a discussion of basic properties of KDE: the convergence rate under various metrics, density derivative estimation, and bandwidth selection. Then, we introduce common approaches to the construction of confidence intervals/bands, and we discuss how to handle bias. Next, we talk about recent advances in the inference of geometric and topological features of a density function using KDE. Finally, we illustrate how one can use KDE to estimate a cumulative distribution function and a receiver operating characteristic curve. We provide R implementations related to this tutorial at the end.