A Parzen-Rosenblatt type density estimator for circular data: exact and asymptotic optimal bandwidths (Preprint)

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Type: Preprint
National /International: International
Title: A Parzen-Rosenblatt type density estimator for circular data: exact and asymptotic optimal bandwidths
Publication Date: 2023-04-19
Authors: - Carlos Tenreiro
Abstract:

For the Parzen-Rosenblatt type density estimator for circular data we prove the existence of a minimiser, \( h_{\mathsf{MISE}}(f;K,n) \), of its exact mean integrated squared error. Under mild conditions we show that it is asymptotically equivalent to the bandwidth \( h_{\mathsf{AMISE}}(f;K,n) \) that minimises the leading terms of the mean integrated squared error expansion, and we obtain the order of convergence of the relative error \( h_{\mathsf{AMISE}}(f;K,n)/h_{\mathsf{MISE}}(f;K,n)-1 \). Some small- and moderate- sample-size comparisons between the two bandwidths are also presented when the underlying density is a mixture of von Mises densities.

Institution: DMUC 23-10
Online version: http://www.mat.uc.pt...prints/eng_2023.html
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