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Overcoming trends in irregularly spaced locations by regional polish – exemplified by estimation of the range of influence between Salmonella Dublin-seropositive cattle herds

  • A. K. ERSBØLL (a1) and B. K. ERSBØLL (a2)

Summary

The aim of the study was to develop a procedure to remove spatial trends in irregularly spaced data, with trends partly due to regional differences. Median polish is often used on regularly spaced (lattice) data where column and row medians are removed. For irregularly spaced data a low-resolution map of the spatial locations is often used where data locations are assigned to the nearest lattice node followed by median polish. In this study regional polish was developed. The inverse distance weighted median was calculated based on observations from locations in the neighbourhood of the actual observation. The regional polish residual is obtained as the difference between the observed value and the weighted median. The regional polish procedure was applied to Salmonella Dublin data showing strong regional trends. Estimation of the range of influence between cattle herds with positive S. Dublin herd status was considerably improved with a stable parameter estimate and reduced standard error.

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Copyright

Corresponding author

*Author for correspondence: Dr A. K. Ersbøll, Department of Large Animal Sciences, Faculty of Life Sciences, University of Copenhagen, Grønnegårdsvej 8, DK-1870 Frederiksberg C, Denmark. (Email: ake@life.ku.dk)

References

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1.Cressie, N. Statistics for Spatial Data. New York: Wiley, 1991.
2.Tukey, JW. Exploratory Data Analysis. Reading: Addison-Wesley, 1977.
3.Cressie, N, Glonek, G. Median based covariogram estimators reduce bias. Statistics and Probability Letters 1984; 2: 299304.
4.Cleveland, WS. Locally weighted regression and smoothing scatterplots. Journal of the American Statistical Association 1979; 74: 829836.
5.Ersbøll, AK, Nielsen, LR. The range of influence between cattle herds is of importance for the local spread of Salmonella Dublin in Denmark. Preventive Veterinary Medicine 2008; 84: 277290.
6.Yin, L, et al. Weighted median filters: a tutorial. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing 1996; 43: 157192.
7.Cressie, N, Hawkins, DM. Robust estimation of the variogram, I. Journal of the International Association for Mathematical Geology 1980; 12: 115125.

Keywords

Overcoming trends in irregularly spaced locations by regional polish – exemplified by estimation of the range of influence between Salmonella Dublin-seropositive cattle herds

  • A. K. ERSBØLL (a1) and B. K. ERSBØLL (a2)

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