Resampling methods for spatial regression models under a class of stochastic designs

The Annals of Statistics · 2006 · Volume 34 · Issue 4

Abstract

In this paper we consider the problem of bootstrapping a class of spatial regression models when the sampling sites are generated by a (possibly nonuniform) stochastic design and are irregularly spaced. It is shown that the natural extension of the existing block bootstrap methods for grid spatial data does not work for irregularly spaced spatial data under nonuniform stochastic designs. A variant of the blocking mechanism is proposed. It is shown that the proposed block bootstrap method provides a valid approximation to the distribution of a class of M-estimators of the spatial regression parameters. Finite sample properties of the method are investigated through a moderately large simulation study and a real data example is given to illustrate the methodology.

Keywords

62G09, 62M30, Block bootstrap method, increasing domain asymptotics, infill sampling, Random field, spatial sampling design, Strong mixing

Enable JavaScript for citation tools and additional paper interactions.