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{{Short description|Concept in statistics mathematics}}
[[Kernel density estimation]] is a [[nonparametric]] technique for [[density estimation]] i.e., estimation of [[probability density function]]s, which is one of the fundamental questions in [[statistics]]. It can be viewed as a generalisation of [[histogram]] density estimation with improved statistical properties. Apart from histograms, other types of density estimators include [[parametric statistics|parametric]], [[spline interpolation|spline]], [[wavelet]] and [[Fourier series]]. Kernel density estimators were first introduced in the scientific literature for [[univariate]] data in the 1950s and 1960s<ref>{{Cite journal| doi=10.1214/aoms/1177728190 | last=Rosenblatt | first=M.| title=Remarks on some nonparametric estimates of a density function | journal=Annals of Mathematical Statistics | year=1956 | volume=27 | issue=3 | pages=832–837| doi-access=free }}</ref><ref>{{Cite journal| doi=10.1214/aoms/1177704472| last=Parzen | first=E.| title=On estimation of a probability density function and mode | journal=Annals of Mathematical Statistics| year=1962 | volume=33 | issue=3 | pages=1065–1076| doi-access=free }}</ref> and subsequently have been widely adopted. It was soon recognised that analogous estimators for multivariate data would be an important addition to [[multivariate statistics]]. Based on research carried out in the 1990s and 2000s, '''multivariate kernel density estimation''' has reached a level of maturity comparable to its univariate counterparts.<ref name="WJ1995">{{Cite book| author1=Wand, M.P | author2=Jones, M.C. | title=Kernel Smoothing | publisher=Chapman & Hall/CRC | ___location=London | year=1995 | isbn = 9780412552700}}</ref><ref name="simonoff1996">{{Cite book| author=Simonoff, J.S. | title=Smoothing Methods in Statistics | publisher=Springer | year=1996 | isbn=9780387947167}}</ref><ref name="chacon2018">{{Cite book| author=Chacón, J.E. and Duong, T. | title=Multivariate Kernel Smoothing and Its applications | publisher=Chapman & Hall/CRC | year=2018 | isbn=9781498763011}}</ref>
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