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Sufficient dimension reduction for spatial point processes directed by Gaussian random fields
Author(s) -
Guan Yongtao,
Wang Hansheng
Publication year - 2010
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2010.00738.x
Subject(s) - linear subspace , subspace topology , sufficient dimension reduction , point process , sliced inverse regression , dimensionality reduction , gaussian , gaussian process , spatial analysis , kriging , dimension (graph theory) , random field , mathematics , algorithm , computer science , reduction (mathematics) , point (geometry) , mathematical optimization , artificial intelligence , statistics , geometry , combinatorics , physics , quantum mechanics
Summary. We develop a sufficient dimension reduction paradigm for inhomogeneous spatial point processes driven by Gaussian random fields. Specifically, we introduce the notion of the k th‐order central intensity subspace. We show that a central subspace can be defined as the combination of all central intensity subspaces. For many commonly used spatial point process models, we find that the central subspace is equivalent to the first‐order central intensity subspace. To estimate the latter, we propose a flexible framework under which most existing benchmark inverse regression methods can be extended to the spatial point process setting. We develop novel graphical and formal testing methods to determine the structural dimension of the central subspace. These methods are extremely versatile in that they do not require any specific model assumption on the correlation structures of the covariates and the spatial point process. To illustrate the practical use of the methods proposed, we apply them to both simulated data and two real examples.