In this paper, we exploit a result in point process theory, knowing the expected value of the $K$-function weighted by the true first-order intensity function. This theoretical result can serve as an estimation method for obtaining the parameters estimates of a specific model, assumed for the data. The motivation is to generally avoid dealing with the complex likelihoods of some complex point processes models and their maximization. This can be more evident when considering the local second-order characteristics, since the proposed method can estimate the vector of the local parameters, one for each point of the analysed point pattern. We illustrate the method through simulation studies for both purely spatial and spatio-temporal point processes.

翻译：本文利用了点过程理论中的一个结果，即由真实一阶强度函数加权的$K$函数的期望值。该理论结果可作为估计方法，用于获取针对数据假设的特定模型参数估计。其动机在于一般情况下避免处理某些复杂点过程模型复杂的似然函数及其最大化问题。当考虑局部二阶特征时，这一优势更为明显，因为所提出的方法能够估计局部参数向量，即针对所分析点模式中的每个点估计一个参数。我们通过纯空间和时空点过程的模拟研究来展示该方法。