Stepwise and stagewise approaches for spatial cluster detection.

Spatial cluster detection is an important tool in many areas such as sociology, botany and public health. Previous work has mostly taken either a hypothesis testing framework or a Bayesian framework. In this paper, we propose a few approaches under a frequentist variable selection framework for spatial cluster detection. The forward stepwise methods search for multiple clusters by iteratively adding currently most likely cluster while adjusting for the effects of previously identified clusters. The stagewise methods also consist of a series of steps, but with a tiny step size in each iteration. We study the features and performances of our proposed methods using simulations on idealized grids or real geographic areas. From the simulations, we compare the performance of the proposed methods in terms of estimation accuracy and power. These methods are applied to the the well-known New York leukemia data as well as Indiana poverty data.