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Nonparametric density estimation over complicated domains
We propose a nonparametric method for density estimation over (possibly complicated) spatial domains. The method combines a likelihood approach with a regularization based on a differential operator. We demonstrate the good inferential properties of the method. Moreover, we develop an estimation pro...
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Published in: | Journal of the Royal Statistical Society. Series B, Statistical methodology Statistical methodology, 2021-04, Vol.83 (2), p.346-368 |
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container_end_page | 368 |
container_issue | 2 |
container_start_page | 346 |
container_title | Journal of the Royal Statistical Society. Series B, Statistical methodology |
container_volume | 83 |
creator | Ferraccioli, Federico Arnone, Eleonora Finos, Livio Ramsay, James O. Sangalli, Laura M. |
description | We propose a nonparametric method for density estimation over (possibly complicated) spatial domains. The method combines a likelihood approach with a regularization based on a differential operator. We demonstrate the good inferential properties of the method. Moreover, we develop an estimation procedure based on advanced numerical techniques, and in particular making use of finite elements. This ensures high computational efficiency and enables great flexibility. The proposed method efficiently deals with data scattered over regions having complicated shapes, featuring complex boundaries, sharp concavities or holes. Moreover, it captures very well complicated signals having multiple modes with different directions and intensities of anisotropy. We show the comparative advantages of the proposed approach over state of the art methods, in simulation studies and in an application to the study of criminality in the city of Portland, Oregon. |
doi_str_mv | 10.1111/rssb.12415 |
format | article |
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subjects | Anisotropy Criminality Density Differential equations differential regularization Domains finite elements Flexibility functional data analysis heat diffusion density estimator Mathematical analysis Nonparametric statistics Operators (mathematics) Regression analysis Regularization Simulation Statistical methods Statistics |
title | Nonparametric density estimation over complicated domains |
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