Comparison of spatial variables over subregions using a block bootstrap

Editor’s Invited Article

Abstract

In environmental and agricultural studies, it is often of interestto compare spatial variables across different regions. Traditional statistical tools that assume independent samples are inadequate because of potential spatial correlations. In this article, spatial dependence is accounted for by a random field model, and a non parametric test is developed to compare the overall distributions of variables in two neighboring regions. Sampling distribution of the test statistic is estimated by a spatial block bootstrap. For illustration, the procedure is applied to study root-lesion nematode populations on a production farm in Wisconsin. Choices of the bootstrap block size are investigated via a simulation study and results of the test are compared to traditional approaches.

Key Words

Empirical distribution function Random field Spatial block bootstrap Two-sample test 

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References

  1. Bühlmann, P. (1994), “Blockwise Bootstrapped Empirical Process for Stationary Sequences,” The Annals of Statistics, 22, 995–1012.MATHCrossRefMathSciNetGoogle Scholar
  2. Conover, W. J. (1999), Practical Nonparametric Statistics (3rd ed.), New York: Wiley.Google Scholar
  3. Doukhan, P. (1994), Mixing: Properties and Examples, New York: Springer.MATHGoogle Scholar
  4. Künsch, H. R. (1989), “The Jackknife and the Bootstrap for General Stationary Observations,” The Annals of Statistics, 17, 1217–1241.MATHCrossRefMathSciNetGoogle Scholar
  5. Lahiri, S. N., Kaiser, M. S., Cressie, N. and Hsu, N. J. (1999), “Prediction of Spatial Cumulative Distribution Functions Using Subsampling” (with discussion), Journal of the American Statistical Association, 94, 86–110.MATHCrossRefMathSciNetGoogle Scholar
  6. Liu, R., and Singh, K. (1992), “Moving Blocks Jackknife and Bootstrap Capture Weak Convergence,” in Exploring the Limits of Bootstrap, eds. R. Lepage and L. Billard, New York: Wiley, pp. 225–248.Google Scholar
  7. Morgan, G. D., MacGuidwin, A. E., Zhu, J., and Binning, L. K. (2002), “Population Dynamics of Root Lesion Nematode Over a Three-Year Potato Crop Rotation,” Agronomy Journal, 94, 1146–1155.CrossRefGoogle Scholar
  8. Olthof, Th. H. A. (1987), “Effects of Fumigants and Systemic Pesticides on Pratylenchus penetrans and Potato Yield,” Journal of Nematology, 19, 424–430.Google Scholar
  9. Townshend, J. L., Potter, J. W., and Willis, C. B. (1978), “Ranges of Distribution of Species of Pratylenchus in Northeastern North America,” Canadian Plant Disease Survey, 58, 80–82.Google Scholar
  10. Webster, R., and Oliver, M. (2001), Geostatistics for Environmental Scientists, New York: Wiley.MATHGoogle Scholar
  11. Zhu, J., and Lahiri, S. N. (2002), “Weak Convergence of Block wise Bootstrapped Empirical Process for Stationary Random Fields With Statistical Applications,” Technical Report 1070, Department of Statistics, University of Wisconsin-Madison.Google Scholar

Copyright information

© International Biometric Society 2004

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of Wisconsin-MadisonMadison
  2. 2.Room 349B Heep CenterTexas A&M UniversityCollege Station

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