A Tutorial on Kernel Density Estimation and Recent Advances

2017/04/12 by Yen‐Chi Chen, Yen-Chi Chen, Chen, Yen-Chi · 32 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Methodology (stat.ME) #Other Statistics (stat.OT) #Statistical Methods and Inference #Topological and Geometric Data Analysis #stat.ME #stat.OT

paper · pdf · doi:10.48550/arxiv.1704.03924

A tutorial paper; accepted to Biostatistics & Epidemiology. Main article: 26 pages, 8 figures. R implementations: 11 pages, generated by Rmarkdown

openalex publication_date 2017/04/12 · arxiv created 2017/09/12 · arxiv updated 2017/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• A note on the estimation of a distribution function and quantiles by a kernel method
• Bootstrap Methods: Another Look at the Jackknife
• On Estimation of a Probability Density Function and Mode

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