Abstract
The pair correlation function is an important and useful tool to explore spatial-temporal point pattern data. It determines the second order characteristics of spatial or temporal process and is often estimated by some nonparametric approach such as kernel smoothing. However, the estimating performance is highly dependent on the estimation of the first order intensity function and it is widely studied only in single point pattern scenario. An inappropriate estimated intensity function may lead to poor estimation for the pair correlation function. In this dissertation, we introduce two nonparametric estimators based on estimating equation technique in a replicated point patterns setting. The two estimators can be easily extended to semiparametric setting to incorporate the covariate(s) information. The two estimators have asymptotic consistency and normality according to our theoretical and simulation results. An empirical study where the points are users' tweets in a Twitter-type data illustrates the application of our estimators.