Multivariate kernel density estimation: Difference between revisions

Revision as of 06:23, 18 December 2019

Revision as of 12:42, 20 December 2019

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: <math>\operatorname{MIAE} (\mathbf{H}) = \operatorname{E}\, \int |\hat{f}_\mathbf{H} (\mathbf{x}) - f(\mathbf{x})| \, d\mathbf{x}.</math>

Its mathematical analysis is considerably more difficult than the MISE ones. In practisepractice, the gain appears not to be significant.<ref>{{cite journal | author1=Hall, P. | author2=Wand, M.P. | title=Minimizing L₁ distance in nonparametric density estimation | journal = Journal of Multivariate Analysis | year=1988 | volume=26 | pages=59–88 | doi=10.1016/0047-259X(88)90073-5}}</ref> The ''L_∞'' norm is the Mean Uniform Absolute Error

: <math>\operatorname{MUAE} (\mathbf{H}) = \operatorname{E}\, \operatorname{sup}_{\mathbf{x}} |\hat{f}_\mathbf{H} (\mathbf{x}) - f(\mathbf{x})|.</math>