Generally, Lasso, Adaptive Lasso, and SCAD are standard approaches in variable selection in the presence of a large number of predictors. In recent years, during intensity function estimation for spatial point processes with a diverging number of predictors, many researchers have considered these penalized methods. But we have discussed a multi-resolution perspective for the variable selection method for spatial point process data. Its advantage is twofold: it not only efficiently selects the predictors but also provides the idea of which points are liable for selecting a predictor at a specific resolution. Actually, our research is motivated by the crime and accident occurrences in St. Louis and its neighborhoods. It is more relevant to select predictors at the local level, and thus we get the idea of which set of predictors is relevant for the occurrences of crime or accident in which parts of St. Louis. We describe the simulation results to justify the accuracy of local-level variable selection during intensity function estimation.

翻译：通常，Lasso、Adaptive Lasso 和 SCAD 是处理大量预测变量时变量选择的标准方法。近年来，在具有发散数量预测变量的空间点过程强度函数估计中，许多研究者已考虑采用这些惩罚方法。但我们探讨了针对空间点过程数据的变量选择方法的多分辨率视角。其优势在于双重性：它不仅能够高效地选择预测变量，还能揭示在特定分辨率下哪些数据点对选择某一预测变量起主导作用。实际上，我们的研究动机源于圣路易斯及其周边地区的犯罪与事故发生率。在局部层级选择预测变量更具实际意义，因此我们得以识别出在圣路易斯哪些区域，哪一组预测变量与犯罪或事故的发生相关联。我们通过模拟结果论证了在强度函数估计过程中局部层级变量选择的准确性。