Below comes from "Ruppert and Wand, Multivariate Locally weighted least squares regression, 1994, p.7 or p.1352 in the Journal"
This is about using Kernel function.
But I don't know what 'the standard results from density estimation' is.
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You have quoted the standard results: your question is its own answer! – whuber Sep 03 '20 at 15:01