On the weak convergence of the kernel density estimator in the uniform topology


The pointwise asymptotic properties of the Parzen-Rosenblatt kernel estimator f̂n of a probability density function f on Rd have received great attention, and so have its integrated or uniform errors. It has been pointed out in a couple of recent works that the weak convergence of its centered and rescaled versions in a weighted Lebesgue Lp space, 1 ≤ p… (More)


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