Abstract
We present a new nonparametric function estimate based on partitions of unity. These density estimates are applicable not only to subsets of R n but to arbitrary metric spaces. They can be used for estimating conditional expectations, and for constructing both nonparametric energy density and nonparametric probability density estimates. We show that under reasonable conditions that the nonparametric density estimates converge in mean square error and under slightly more restrictive conditions that they converge in integrated mean square error. A computer graphics application is presented.
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