Abstract
Lasso and Dantzig selector are standard procedures able to perform variable selection and estimation simultaneously. This paper is concerned with extending these procedures to spatial point process intensity estimation. We propose adaptive versions of these procedures, develop efficient computational methodologies and derive asymptotic results for a large class of spatial point processes under an original setting where the number of parameters, i.e. the number of spatial covariates considered, increases with the expected number of data points. Both procedures are compared theoretically, in a simulation study, and in a real data example.
Acknowledgements
We thank the editor, associate editor, and two reviewers for the constructive comments. The research of J.-F. Coeurjolly is supported by the Natural Sciences and Engineering Research Council of Canada. J.-F. Coeurjolly would like to thank Université du Québec à Montréal for the excellent research conditions he received these last years. The research of A. Choiruddin is supported by the Direktorat Riset, Teknologi, dan Pengabdian Kepada Masyarakat, Direktorat Jenderal Pendidikan Tinggi, Riset, dan Teknologi, Kementerian Pendidikan, Kebudayaan, Riset, dan Teknologi Republik Indonesia. The BCI soils data sets were collected and analyzed by J. Dalling, R. John, K. Harms, R. Stallard and J. Yavitt with support from NSF DEB021104,021115, 0212284,0212818 and OISE 0314581, and STRI Soils Initiative and CTFS and assistance from P. Segre and J. Trani.
Citation
Achmad Choiruddin. Jean-François Coeurjolly. Frédérique Letué. "Adaptive lasso and Dantzig selector for spatial point processes intensity estimation." Bernoulli 29 (3) 1849 - 1876, August 2023. https://doi.org/10.3150/22-BEJ1523
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