论文标题
推断可能高维的不均匀吉布斯点过程
Inference for possibly high-dimensional inhomogeneous Gibbs point processes
论文作者
论文摘要
Gibbs点过程（GPP）构成了一类庞大而灵活的空间点过程，两者之间具有明确的依赖性。它们可以建模有吸引力的和排斥的点模式。特征选择程序是高维统计建模中的重要主题。在本文中，提出了使用凸的复合可能性方法正规化的，并提出了非凸位惩罚函数来处理可能高维的不均匀GPP的统计推断。复合的可能性既包含伪样的样子和逻辑复合可能性。我们特别研究了协变量数量随着观察域的增加而发散的设置。在空间GPP和罚款功能上提供的某些条件下，我们表明Oracle财产，一致性和渐近正态性。我们的结果还涵盖了填补文献中较大空白的低维情况。通过模拟实验，我们验证了理论结果，最后，对热带林业数据集的应用说明了提出的方法的使用。
Gibbs point processes (GPPs) constitute a large and flexible class of spatial point processes with explicit dependence between the points. They can model attractive as well as repulsive point patterns. Feature selection procedures are an important topic in high-dimensional statistical modeling. In this paper, composite likelihood approach regularized with convex and non-convex penalty functions is proposed to handle statistical inference for possibly high-dimensional inhomogeneous GPPs. The composite likelihood incorporates both the pseudo-likelihood and the logistic composite likelihood. We particularly investigate the setting where the number of covariates diverges as the domain of observation increases. Under some conditions provided on the spatial GPP and on the penalty functions, we show that the oracle property, the consistency and the asymptotic normality hold. Our results also cover the low-dimensional case which fills a large gap in the literature. Through simulation experiments, we validate our theoretical results and finally, an application to a tropical forestry dataset illustrates the use of the proposed approach.
