Title: A Tutorial on Kernel Density Estimation and Recent Advances,
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.