Spatial Analysis. Kanti V. Mardia

href="#fb3_img_img_95fe17c9-c992-5833-bb08-6b3dc046623c.png" alt="images"/> locations.Table 1.4 Gravimetric data: local gravity measurements in Quebec, Canada.Table 1.5 Semivariograms in each direction for the gravimetric data.Table 1.6 Soil data: surface pH in

on an

grid.Table 1.7 Mercer–Hall wheat yield (in lbs.) for 20 (rows)

25 (columns) ag...Table 1.8 Aggregated Mercer–Hall wheat data for plots aggregated into block...

      2 Chapter 2Table 2.1 Some radial covariance functions.Table 2.2 Special cases of the Matérn covariance function in 2.34 for half‐...Table 2.3 Some examples of stationary covariance functions

on the circle,...

      3 Chapter 3Table 3.1 Self‐similar random fields with spectral density

: some particul...

      4 Chapter 5Table 5.1 Parameter estimates (and standard errors) for the bauxite data us...Table 5.2 Parameter estimates (and standard errors) for the elevation data ...Table 5.3 Parameter estimates (with standard errors in parentheses) for Vec...

      5 Chapter 7Table 7.1 Notation used for kriging at the data sites

, and at the predict...Table 7.2 Various methods of determining the kriging predictor

, where

c...Table 7.3 Comparison between the terminology and notation of this book for ...

      6 Appendix ATable A.1 Types of domain.Table A.2 Domains for Fourier transforms and inverse Fourier transforms in ...Table A.3 Three types of boundary condition for a one‐dimensional set of da...Table A.4 Some examples of Toeplitz, circulant, and folded circulant matric...Table A.5 First and second derivatives of

and

with respect to

and

....

      List of Illustrations

      1 Chapter 1Figure 1.1 Fingerprint of R A Fisher, taken from Mardia's personal collectio...Figure 1.2 Elevation data: (a) raw plot giving the elevation at each site an...Figure 1.3 Panels (a), (b), and (c) show interpolated plots for the elevatio...Figure 1.4 Bauxite data: (a) raw plot giving the ore grade at each site and ...Figure 1.5 Landsat data (

pixels): image plot.Figure 1.6 Synthetic Landsat data: image plot.Figure 1.7 Typical semivariogram, showing the range, nugget variance, and si...Figure 1.8 Angle convention for polar coordinates. Angles are measured clock...Figure 1.9 Fingerprint section data (218 pixels wide by 356 pixels high): (a...Figure 1.10 Elevation data: (a) directional semivariograms and (b) omnidirec...Figure 1.11 Bauxite data: (a) directional semivariograms and (b) omnidirecti...Figure 1.12 Directional semivariograms for (a) the Landsat data and (b) the ...Figure 1.13 Gravimetric data: (a) bubble plot and (b) directional semivariog...Figure 1.14 Soil data: (a) bubble plot and (b) directional semivariograms.Figure 1.15 Mercer–Hall wheat data: log–log plot of variance vs. block size....

      2 Chapter 2Figure 2.1 Matérn covariance functions for varying index parameters. The ran...

      3 Chapter 3Figure 3.1 Examples of radial semivariograms: the power schemes

for

and ...Figure 3.2 A linear semivariogram with a nugget effect:

.

      4 Chapter 4Figure 4.1 Panels (a) and (b) illustrate the first‐order basic and full neig...Figure 4.2 Three notions of “past” of the origin in

: (a) quadrant past (

)...Figure 4.3 (a) First‐order basic neighborhood (nbhd) of the origin ○ in

di...Figure 4.4 (a) First‐order full neighborhood (nbhd) of the origin ○ in

dim...

      5 Chapter 5Figure 5.1 Bauxite data: Bubble plot and directional semivariograms.Figure 5.2 Elevation data: Bubble plot and directional semivariograms.Figure 5.3 Bauxite data: Profile log‐likelihoods together with 95% confidenc...Figure 5.4 Bauxite data: sample isotropic semivariogram values and fitted Ma...Figure 5.5 Elevation data: Profile log‐likelihoods together with 95% confide...Figure 5.6 Unilateral lexicographic neighborhood of full size

for lattice ...Figure 5.7 Profile log‐likelihoods for self‐similar models of intrinsic orde...

      6 Chapter 6Figure 6.1 Mercer–Hall data: bubble plot. See Example 6.1 for an interpretat...Figure 6.2 A plot of the sample and two fitted covariance functions (“biased...Figure 6.3 A plot of the sample and two fitted covariance functions (“fold‐m...Figure 6.4 Relative efficiency of the composite likelihood estimator in AR(1...

      7 Chapter 7Figure 7.1 Kriging predictor for

data points assumed to come from a statio...Figure 7.2 Kriging predictor for

data points assumed to come from a statio...Figure 7.3 Panel (a) shows the interpolated kriging surface for the elevatio...Figure 7.4 Panel (a) shows a contour plot for the kriged surface fitted to t...Figure 7.5 Kriging predictor and kriging standard errors for

data points a...Figure 7.6 Panel (a) shows the interpolated kriging surface for the gravimet...Figure 7.7 Kriging predictors for Example 7.6. For Panel (a), the kriging pr...Figure 7.8 Deformation of a square (a) into a kite (b)