Spatial Statistics in the Presence of Location Error with an Application to Remote Sensing of the Environment

Techniques for the analysis of spatial data have, to date, tended to ignore any effect caused by error in specifying the spatial locations at which measurements are recorded. This paper reviews the methods for adjusting spatial inference in the presence of data-location error, particularly for data that have a continuous spatial index (geostatistical data). New kriging equations are developed and evaluated based on a simulation experiment. They are also applied to remote-sensing data from the Total Ozone Mapping Spectrometer instrument on the Nimbus-7 satellite, where the location error is caused by assignment of the data to their nearest grid-cell centers. The remote-sensing data measure total column ozone (TCO), which is important for protecting the Earth's surface from ultraviolet and other radiation.

[1]  Siemen's Ozonizer.  Ozone , 1868, Reactions Weekly.

[2]  D.Sc. Joseph Berkson.  Are there Two Regressions , 1950 .

[3]  D.Sc. Joseph Berkson.  Are there Two Regressions , 1950 .

[4]  G. Matheron.  Principles of geostatistics , 1963 .

[5]  Charles J. Stone,et al.  On a Theorem by Dobrushin , 1968 .

[6]  J. P. Chilès,et al.  How to Adapt Kriging to Non-Classical Problems: Three Case Studies , 1976 .

[7]  Donald Geman,et al.  Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[8]  J. London.  The observed distribution of atmospheric ozone and its variations , 1985 .

[9]  David A. Harville,et al.  Decomposition of Prediction Error , 1985 .

[10]  F. Bookstein.  Size and Shape Spaces for Landmark Data in Two Dimensions , 1986 .

[11]  J. Van Dyck,et al.  Statistical Analysis of Earthquake Catalogs for Seismic Hazard , 1987 .

[12]  D. Ruppert,et al.  Transformation and Weighting in Regression , 1988 .

[13]  Deborah Burr,et al.  On Errors-in-Variables in Binary Regression—Berkson Case , 1988 .

[14]  Noel A Cressie,et al.  On the stability of the geostatistical method , 1992 .

[15]  Noel A Cressie,et al.  Statistics for Spatial Data. , 1992 .

[16]  Mike Rees,et al.  5. Statistics for Spatial Data , 1993 .

[17]  Robert Haining,et al.  Error Propagation Through Map Operations , 1993 .

[18]  Peter Kielland,et al.  On estimating map model errors and GPS position errors: Applying more science to the art of navigation , 1994 .

[19]  P. Diggle.  Analysis of Longitudinal Data , 1995 .

[20]  P. Atkinson.  Simulating Locational Error in Field-Based Measurements of Reflectance , 1997 .

[21]  Daniel A. Griffith,et al.  Error Propagation Modelling in Raster GIS: Overlay Operations , 1998, Int. J. Geogr. Inf. Sci..

[22]  T. C. Haas,et al.  Model-based geostatistics - Discussion , 1998 .

[23]  John George Gabrosek,et al.  The effect of locational uncertainty in geostatistics , 1999 .

[24]  Asymptotic properties in space and time of an estimator in nonlinear functional errors-in-variables models , 1999 .

[25]  J. Chilès,et al.  Geostatistics: Modeling Spatial Uncertainty , 1999 .

[26]  John Noel A. C Gabrosek,et al.  The Effect on Attribute Prediction of Location Uncertainty in Spatial Data , 2002 .

[27]  Tapabrata Maiti,et al.  Analysis of Longitudinal Data (2nd ed.) (Book) , 2004 .