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.
Original language | English |
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Pages (from-to) | 1774-1813 |
Number of pages | 40 |
Journal | Annals of Statistics |
Volume | 34 |
Issue number | 4 |
DOIs | |
State | Published - Aug 2006 |
Keywords
- Block bootstrap method
- Increasing domain asymptotics
- Infill sampling
- Random field
- Spatial sampling design
- Strong mixing