Multivariate kernel density estimation: Difference between revisions

Revision as of 13:19, 14 March 2020

Revision as of 13:19, 14 March 2020

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

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

where * is the [[convolution]] operator between two functions, and