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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Bibliographic Details
Published in:Journal of the Royal Statistical Society. Series B, Statistical methodology Statistical methodology, 2021-04, Vol.83 (2), p.346-368
Main Authors: Ferraccioli, Federico, Arnone, Eleonora, Finos, Livio, Ramsay, James O., Sangalli, Laura M.
Format: Article
Language:English
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
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Summary: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.
ISSN:1369-7412
1467-9868
DOI:10.1111/rssb.12415