A Parzen–Rosenblatt type density estimator for circular data: exact and asymptotic optimal bandwidths

Carlos Tenreiro

Communications in Statistics - Theory and Methods, 2024, vol. 53, issue 20, 7436-7452

Abstract: For the Parzen–Rosenblatt type density estimator for circular data, we prove the existence of a minimizer, hMISE(f;K,n), of its exact mean integrated squared error (MISE) and show that it is asymptotically equivalent to the bandwidth hAMISE(f;K,n) that minimizes the leading terms of the MISE, together with the order of convergence of the relative error hAMISE(f;K,n)/hMISE(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.

Date: 2024
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DOI: 10.1080/03610926.2023.2264996

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