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A Tutorial on Kernel Density Estimation and Recent Advances

arXiv 1704.03924 ↗First posted 12 Apr 2017stat.ME stat.OTcited by 101

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Abstract (arXiv)

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.

Key facts. Cited by 101 papers in the map (data through 14 Oct 2026). First posted on arXiv 12 Apr 2017.

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Citing papers per year: 2021: 10; 2022: 15; 2023: 22; 2024: 16; 2025: 23; 2026: 15.

101 papers.

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  11. 2021Stochastic Physics-Informed Neural Ordinary Differential Equationscited by 19
  12. 2023Learning to (Learn at Test Time)cited by 17
38 more
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  4. 2021Assessing the Reliability of Deep Learning Classifiers Through Robustness Evaluation and Operational Profilescited by 11
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  10. 2023Kernel Density Estimation for Multiclass Quantificationcited by 8
  11. 2024MORPH: Towards Automated Concept Drift Adaptation for Malware Detectioncited by 8
  12. 2023Bounded KRnet and its applications to density estimation and approximationcited by 7
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  14. 2023Noise-Free Sampling Algorithms via Regularized Wasserstein Proximalscited by 7
  15. 2024Score-based Neural Ordinary Differential Equations for Computing Mean Field Control Problemscited by 7
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