The Annals of Statistics

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

S. N. Lahiri and Jun Zhu

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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.

Article information

Ann. Statist., Volume 34, Number 4 (2006), 1774-1813.

First available in Project Euclid: 3 November 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G09: Resampling methods
Secondary: 62M30: Spatial processes

Block bootstrap method increasing domain asymptotics infill sampling random field spatial sampling design strong mixing


Lahiri, S. N.; Zhu, Jun. Resampling methods for spatial regression models under a class of stochastic designs. Ann. Statist. 34 (2006), no. 4, 1774--1813. doi:10.1214/009053606000000551.

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