Publication
A Parzen-Rosenblatt type density estimator for circular data: exact and asymptotic optimal bandwidths
| Summary: | For the Parzen-Rosenblatt type density estimator for circular data we prove the existence of a minimizer, h_{MISE}(f;K,n), of its exact mean integrated squared error (MISE) and show that it is asymptotically equivalent to the bandwidth h_{AMISE}(f;K,n) that minimizes the leading terms of the MISE, together with the order of convergence of the relative error h_{AMISE}(f;K,n)/h_{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. |
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| Main Authors: | Tenreiro, Carlos |
| Subject: | Parzen-Rosenblatt type density estimator circular data exact and asymptotic optimal bandwidths |
| Year: | 2024 |
| Country: | Portugal |
| Document type: | article |
| Access type: | embargoed access |
| Associated institution: | Universidade de Coimbra |
| Language: | English |
| Origin: | Estudo Geral - Universidade de Coimbra |
| Summary: | For the Parzen-Rosenblatt type density estimator for circular data we prove the existence of a minimizer, h_{MISE}(f;K,n), of its exact mean integrated squared error (MISE) and show that it is asymptotically equivalent to the bandwidth h_{AMISE}(f;K,n) that minimizes the leading terms of the MISE, together with the order of convergence of the relative error h_{AMISE}(f;K,n)/h_{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. |
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