Statistics for Spatial Data (Wiley Series in Probability and Statistics) by Cressie Noel

Author:Cressie, Noel [Cressie, Noel]
Language: eng
Format: azw3
ISBN: 9781119115175
Publisher: Wiley
Published: 2015-03-23T04:00:00+00:00

Mercer and Hall carried out some preliminary analyses of the data; further exploratory spatial analyses are presented in Section 4.5. In summary, a stem-and-leaf plot of the 500 data indicate that the data are Gaussian, although plots of column median versus column number and row median versus row number show a disquieting spatial periodicity. Further discussion of this is given in McBratney and Webster (1981) and in Section 4.5.

7.1.2† Spatial Lattice Models

In spite of the heterogeneities in the field (e.g., presence of “lands,” thistles in 187 out of 500 plots) and periodicities in the trend, most lattice models fitted to the data in Figure 7.1 assume constant large-scale variation, hoping that (homogeneous) spatial dependence parameters can explain all of the spatial variation. In fact, commenting on their frequency curve of all 500 data, Mercer and Hall (1911) say that “since the [frequency] curve fits the [Gaussian] one as well as may be expected … we may conclude that the material is fairly homogeneous.” From the analysis given in Section 4.5, it is clear that their conclusion is not a proper one. Nevertheless, I shall use these data, and the Gaussian models fitted to them, to illustrate maximum likelihood estimation and likelihood ratio testing.

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