## The Annals of Statistics

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

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 3 November 2006

https://projecteuclid.org/euclid.aos/1162567633

Digital Object Identifier
doi:10.1214/009053606000000551

Mathematical Reviews number (MathSciNet)
MR2283717

Zentralblatt MATH identifier
1246.62117

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

#### Citation

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. https://projecteuclid.org/euclid.aos/1162567633

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