Fast Block Variance Estimation Procedures for Inhomogeneous Spatial Point Processes

We introduce two new variance estimation procedures by using non-overlapping and overlapping blocks, respectively. The non-overlapping block (NOB) estimator can be viewed as the limit of the thinned block bootstrap (TBB) estimator recently proposed in Guan and Loh (2007), by letting the number of thinned processes and bootstrap samples therein both increase to infinity. Compared to the latter, the NOB estimator can be obtained much faster since it does not require any thinning or bootstrap steps, and is more stable since it is the limit of the latter by using an infinite number of thinnings and bootstrap samples. The overlapping block estimator further improves the performance of the NOB with a modest increase in computational time. A simulation study demonstrates the superiority of the proposed estimators over the TBB estimator. Some key words: Block Variance Estimator; Inhomogeneous Spatial Poisson Process; Thinning. Short Title. Block Variance Estimator for Inhomogeneous Point Processes.