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.

翻译：Lasso和Dantzig选择器是标准程序,能够同时进行可变的选择和估计。本文件涉及将这些程序扩大到空间点进程强度估计。我们提议这些程序的适应性版本,制定高效的计算方法,并在最初设定参数(即所考虑的空间共变数)与预期数据点数相比增加的情况下,为一大批空间点进程产生无症状结果。两种程序都是在理论上、模拟研究和真实数据实例中比较的。