Multivariate kernel density estimation: Difference between revisions

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{{Merge to|Kernel density estimation|date=September 2010}}

[[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 | pages=832–837}}</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 | pages=1065–1076}}</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 theirits univariate counterparts.<ref name="simonoff1996">{{Cite book| author=Simonoff, J.S. | title=Smoothing Methods in Statistics | publisher=Springer | year=1996 | isbn=0-387-94716-7}}</ref>

==Motivation==