Estimating Weighted Integrals of the Second-Order Intensity of a Spatial Point Process
针对二维平稳各向同性点过程，提出二阶强度函数加权积分的无偏估计量及快速近似算法，并用于点过程数据平滑、二阶强度傅里叶变换估计及空间关联性检验。
SUMMARY This paper considers the nonparametric estimation of the integral J=∫0Ttλ2(t)φ(t)dt where λ2(t) is the unknown second-order intensity function of a two-dimensional stationary isotropic point process observed in some region and φ(t) is known for t ϵ [0, T]. An unbiased estimator of J is derived, and a computationally fast approximation to it is proposed. The estimator is then used to obtain a kernel method for smoothing point process data, a new estimator of the Fourier transform of the second-order intensity and some tests for spatial association between a point process and another stochastic process.