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

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

2006-11-09

arxiv.org/abs/math/0611261v1

Annals of Statistics 2006, Vol. 34, No. 4, 1774-1813

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053606000000551 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053606000000551

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.

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