Multivariate kernel density estimation: Difference between revisions

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'''Multivariate kernel density estimation'''

[[Statistics]] is a field of quantitative analysis concerned with quantifying uncertainty. The main building block of statistical analysis is a [[random variable]]. A random variable is a [[mathematical|mathematics]] function which assigns a numerical value to each possible value of

the variable of interest. The complete behaviour of a random variable is contained in its [[distribution function]]. For [[continuous]] random variables, the partial derivative of the distribution function is known as [[probability density function]] or pdf. So [[density estimation]] is a fundamental question in statistics.

[[Density estimation|estimating]] is a fundamental question in the field of [[statistics]].

In [[statistics]], '''kernel density estimation''' (or '''Parzen window''' method, named after [[Emanuel Parzen]]) is a [[Non-parametric statistics|non-parametric]] way of [[Density estimation|estimating]] the [[probability density function]] of a [[random variable]]. As an illustration, given some data about a [[statistical sample|sample]] of a [[Statistical population|population]], kernel density estimation makes it possible to [[extrapolation|extrapolate]] the data to the entire population.

[[Kernel density estimation]] is one of the most popular techniques for density estimation. It can be viewed as a generalisation of [[histogram]] density estimation with improved statistical properties.

== Motivation ==

Kernel density estimators were first introduced in the scientific literature for [[univariate]] data by

<ref>{{cite journal|doi=10.1214/aoms/1177728190|last=Rosenblatt|first=M.|title=Remarks on some nonparametric estimates of a density function |url=http://projecteuclid.org/euclid.aoms/1177728190|journal=[[Annals of Mathematical Statistics]]|year=1956|volume=27|pages=832-837}}</ref>