TwinKernel Estimation for Point Process Intensity Functions: Adaptive Nonparametric Methods via Orbital Regularity
点过程强度函数的孪生核估计:基于轨道正则性的自适应非参数方法
We develop TwinKernel methods for nonparametric estimation of intensity functions of point processes. Building on the general TwinKernel framework and combining it with martingale techniques for counting processes, we construct estimators that adapt to orbital regularity of the intensity function. Given a point process $N$ with intensity $λ$ and a cyclic group $G = \langle\varphi\rangle$ acting on the time/space domain, we transport kernels along group orbits to create a…