Nonparametric Block Bootstrap for Spatial Data

Abstract

In this talk, a stationary strong-mixing random field is considered. Under a large-sample scheme that is a mixture of the infill and increasing domain asymptotics, a functional central limit theorem is established for the empirical processes of the random field. Further, a block bootstrap to the samples is applied and under suitable conditions, the bootstrapped empirical process is shown to converge weakly to the same limiting Gaussian process almost surely. Extension to multivariate random fields is also given. Based on the theory, two statistical procedures are developed: one is hypothesis testing for comparing overall distributions of spatial variables in two neighboring regions, and the other is inference for temporal changes according to spatial data observed repeatedly over a fixed number of time points. For illustration, these procedures are applied to study root-lesion nematode populations across space and over time in a Wisconsin production field. Choices of the bootstrap block sizes are investigated via simulations and the results of these procedures are compared to traditional approaches.