Multivariate kernel density estimation: Difference between revisions

Revision as of 15:17, 2 July 2015

Revision as of 10:17, 3 July 2015

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==Asymptotic analysis==

In the optimal bandwidth selection section, we introduced the MISE. Its construction relies on the [[expected value]] and the [[variance]] of the density esimatorestimator<ref name="WJ1995"/>{{rp|97}}

:<math>\operatorname{E} \hat{f}(\bold{x};\bold{H}) = K_\bold{H} * f (\bold{x}) = f(\bold{x}) + \frac{1}{2} m_2(K) \int \operatorname{tr} (\bold{H} \operatorname{D}^2 f(\bold{x})) \, d\bold{x} + O(\operatorname{tr} \, \bold{H}^2)</math>