×

Distribution of increases in residual log likelihood for nested spatial models. (English) Zbl 1093.62089

Summary: We review nested relationships between models in the Matérn family of spatial models. The problem of comparing nested statistical models is straightforward in regular parametric problems via the likelihood ratio statistics and its asymptotic distribution. Here we examine the distribution of increments in the residual log likelihood between nested spatial models when the null hypothesis is that the spatial structure is a convex combination of white noise and the de Wijs process [H. J. de Wijs, J. R. Netherlands Geol. Mining Soc. 13, 365–375 (1951); ibid. 13, 124–125 (1953)], also known by its logarithmic covariance function. This study is carried out by simulation of spatial processes and the important aspects of this work include how to simulate a spatial process of order 0, the lack of strong bias in the estimates of variance components, and the validity of the usual asymptotic results for nested spatial models examined here.

MSC:

62M30 Inference from spatial processes
62H11 Directional data; spatial statistics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Clifford , D. ( 2004 ). The Nature of Spatial Variation in Crop Yields . PhD thesis, The University of Chicago, Chicago, USA .
[2] Clifford D., J. Computat. Graph. Statist. 14 pp 155– (2005) · doi:10.1198/106186005X27626
[3] Clifford D., J. Agricultural Sci. (2006)
[4] de Wijs H. J., J. Roy. Netherlands Geolog. Mining Soc. 13 pp 365– (1951)
[5] de Wijs H. J., J. Roy. Netherlands Geologi. Mining Soc. 15 pp 125– (1953)
[6] Materon G., J. Appl. Probab. 5 pp 439– (1973) · Zbl 0324.60036 · doi:10.2307/1425829
[7] McCullagh P., Proc. Roy. Soc. A. (2006)
[8] Stein M. L., Interpolation of Spatial Data: Some Theory of Kriging (1999) · Zbl 0924.62100
[9] Wahba G., Spline Models for Observational Data (1990) · Zbl 0813.62001
[10] Whittle P., Biometrika 49 pp 434– (1954)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.