Journal
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
Volume 77, Issue 3, Pages 699-726Publisher
WILEY-BLACKWELL
DOI: 10.1111/rssb.12084
Keywords
Hutchinson's trace approximations; Incomplete Cholesky decomposition; Lanczos algorithm; Matrix-free computations; Nearest neighbour adjustment; Residual maximum likelihood; Variety trials; de Wijs process
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Funding
- National Science Foundation [DMS 0906300, DMS 1254840]
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We consider sparse spatial mixed linear models, particularly those described by Besag and Higdon, and develop an h-likelihood method for their statistical inference. The method proposed allows for singular precision matrices, as it produces estimates that coincide with those from the residual maximum likelihood based on appropriate differencing of the data and has a novel approach to estimating precision parameters by a gamma linear model. Furthermore, we generalize the h-likelihood method to include continuum spatial variations by making explicit use of scaling limit connections between Gaussian intrinsic Markov random fields on regular arrays and the de Wijs process. Keeping various applications of spatial mixed linear models in mind, we devise a novel sparse conjugate gradient algorithm that allows us to achieve fast matrix-free statistical computations. We provide two applications. The first is an extensive analysis of an agricultural variety trial that brings forward various new aspects of nearest neighbour adjustment such as effects on statistical analyses to changes of scale and use of implicit continuum spatial formulation. The second application concerns an analysis of a large cotton field which gives a focus to matrix-free computations. The paper closes with some further considerations, such as applications to irregularly spaced data, use of the parametric bootstrap and some generalizations to the Gaussian Matern mixed effect models.
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