Sufficient Dimension Reduction for Spatial Point Processes Directed by Gaussian Random Fields

35 Pages Posted: 4 Dec 2009

See all articles by Yongtao Guan

Yongtao Guan

University of Miami - Department of Management Science

Hansheng Wang

Peking University - Guanghua School of Management

Date Written: December 2, 2009

Abstract

We develop a sufficient dimension reduction paradigm for inhomogeneous spatial point processes driven by a Gaussian random fields. Specifically, we introduce the notion of the kth-order Central Intensity Subspace. We show that a Central Subspace (Cook, 1998) 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 proposed methods, we apply them to both simulated data and two real examples.

Keywords: Central Intensity Subspace, Central Subspace, Inhomogeneous, Spatial Point Process, Inverse Regression

JEL Classification: C10, C13

Suggested Citation

Guan, Yongtao and Wang, Hansheng, Sufficient Dimension Reduction for Spatial Point Processes Directed by Gaussian Random Fields (December 2, 2009). Available at SSRN: https://ssrn.com/abstract=1516982 or http://dx.doi.org/10.2139/ssrn.1516982

Yongtao Guan

University of Miami - Department of Management Science ( email )

United States

Hansheng Wang (Contact Author)

Peking University - Guanghua School of Management ( email )

Peking University
Beijing, Beijing 100871
China

HOME PAGE: http://hansheng.gsm.pku.edu.cn

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