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 the setting where the number of parameters, i.e. the number of spatial covariates considered, increases with the volume of the observation domain. Both procedures are compared theoretically and in a simulation study.

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。我们建议采用这些程序的适应性版本,制定高效的计算方法,并在参数数量(即考虑的空间共变数)随观测域量的增加而增加的环境下,为一大批空间点进程得出无症状结果。两种程序在理论上和模拟研究中都进行了比较。