Sufficient Dimension Reduction for Spatial point Processes Directed by Gaussian Random Fields
Year: 2010
Type: article
Abstract: 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 kth-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.
Authors: Yongtao Guan, Hansheng Wang
Institution: Yale University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1198279745, 收缩估计作为模型选择方法的有效性研究, LTREB: Long-Term Studies of Seedling and Small Sapling Community Dynamics in a Neotropical Forest, What Causes Large Local-Scale Variation in Tree Diversity in a Neotropical Forest? An Experimental Approach, Habitat Variation in the Demography and Life History of Tropical Trees, G3772627221, Dynamics of a Neotropical Forest: The First Decade, Demographic Analysis of a Tropical Forest in Panama, The Structure and Dynamics of a Tropical Forest, G6242140455, The Neutral Theory of Biodiversity and Biogeography: "New Theoretical Approaches", The Dynamics of a Neotropical Forest: The 1995 Recensus Including Seedling and Small Sapling Populations, The Dynamics of a Neotropical Forest: the 2005 Recensus and the Annual Seedling and Small Sapling Census, CAREER: New Statistical Methods for Massive Spatial, Temporal and Spatial-Temporal Processes, Theoretical and Empirical Studies of Seed and Pollen Dispersal in Tropical Trees, Spatial Point Pattern Analysis Using Composite Likelihood, Impact of Logging on the Demography and Population Genetics of Mahogany in Bolivia
OpenAlex ID: W3121439794