Multivariate kernel density estimation: Difference between revisions

Revision as of 14:19, 7 September 2019

Revision as of 10:34, 10 November 2019

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==Definition==

The previous figure is a graphical representation of kernel density estimate, which we now define in an exact manner. Let '''x'''₁, '''x'''₂, …..., '''x'''_''n'' be a [[random sample|sample]] of ''d''-variate [[random vector]]s drawn from a common distribution described by the [[probability density function|density function]] ''ƒ''. The kernel density estimate is defined to be

: <math>

\hat{f}_\mathbf{H}(\mathbf{x})= \frac1n \sum_{i=1}^n K_\mathbf{H} (\mathbf{x} - \mathbf{x}_i)