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The Scientific World Journal
Volume 2014, Article ID 698296, 23 pages
http://dx.doi.org/10.1155/2014/698296
Research Article

Testing Spatial Symmetry Using Contingency Tables Based on Nearest Neighbor Relations

Department of Mathematics, Koç University, Sarıyer, 34450 Istanbul, Turkey

Received 23 August 2013; Accepted 22 October 2013; Published 19 January 2014

Academic Editors: A. Barra, S. Casado, and J. Pacheco

Copyright © 2014 Elvan Ceyhan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. D. A. Coomes, M. Rees, and L. Turnbull, “Identifying aggregation and association in fully mapped spatial data,” Ecology, vol. 80, no. 2, pp. 554–565, 1999. View at Google Scholar · View at Scopus
  2. E. C. Pielou, “Segregation and symmetry in two-species populations as studied by nearest-neighbor relation-ships,” Journal of Ecology, vol. 49, no. 2, pp. 255–269, 1961. View at Google Scholar
  3. P. M. Dixon, “Nearest-neighbor contingency table analysis of spatial segregation for several species,” Ecoscience, vol. 9, no. 2, pp. 142–151, 2002. View at Google Scholar · View at Scopus
  4. M. Kulldorff, “Tests of spatial randomness adjusted for an inhomogeneity: a general framework,” Journal of the American Statistical Association, vol. 101, no. 475, pp. 1289–1305, 2006. View at Publisher · View at Google Scholar · View at Scopus
  5. A. J. Baczkowski and K. V. Mardia, “A test of spatial symmetry with general application,” Communications in Statistics, vol. 19, no. 2, pp. 555–572, 1990. View at Google Scholar
  6. M. Sherman, Spatial Statistics and Spatio-Temporal Data. Covariance Functions and Directional Properties, John Wiley & Sons, Chichester, UK, 2011.
  7. P. Mossay and P. M. Picard, “On spatial equilibria in a social interaction model,” Journal of Economic Theory, vol. 146, no. 6, pp. 2455–2477, 2011. View at Publisher · View at Google Scholar · View at Scopus
  8. L. Scaccia and R. J. Martin, “Testing axial symmetry and separability of lattice processes,” Journal of Statistical Planning and Inference, vol. 131, no. 1, pp. 19–39, 2005. View at Publisher · View at Google Scholar · View at Scopus
  9. P. M. Dixon, Testing Spatial Independence in Multivariate Point Processes, vol. 2215 of Institute of Statistics Mimeo, Raleigh, NC, USA, 1992.
  10. P. Dixon, “Testing spatial segregation using a nearest-neighbor contingency table,” Ecology, vol. 75, no. 7, pp. 1940–1948, 1994. View at Google Scholar · View at Scopus
  11. T. R. Meagher and D. S. Burdick, “The use of nearest neighbor frequency analysis in studies of association,” Ecology, vol. 61, no. 5, pp. 1253–1255, 1980. View at Google Scholar
  12. E. Ceyhan, “On the use of nearest neighbor contingency tables for testing spatial segregation,” Environmental and Ecological Statistics, vol. 17, no. 3, pp. 247–282, 2010. View at Publisher · View at Google Scholar · View at Scopus
  13. W. J. Conover, Practical Nonparametric Statistics, John Wiley & Sons, 3rd edition, 1999.
  14. A. H. Bowker, “A test for symmetry in contingency tables,” Journal of the American Statistical Association, vol. 43, no. 244, pp. 572–574, 1948. View at Google Scholar · View at Scopus
  15. P. J. Diggle, “On parameter estimation and goodness-of-fit testing for spatial point patterns,” Biometrics, vol. 35, no. 1, pp. 87–101, 1979. View at Google Scholar · View at Scopus
  16. D. Yates, D. Moore, and G. McCabe, Nonparametrics: Statistical Methods Based on Rank, W.H. Freeman, New York, NY, USA, 1st edition, 1999.
  17. A. Agresti, “A survey of exact inference for contingency tables,” Statistical Science, vol. 7, no. 1, pp. 131–153, 1992. View at Publisher · View at Google Scholar
  18. E. Ceyhan, “Exact inference for testing spatial patterns by nearest neighbor contingency tables,” Journal of Probability and Statistical Science, vol. 8, no. 1, pp. 45–68, 2010. View at Google Scholar
  19. K. D. Tocher, “Extension of the Neyman-Pearson theory of tests to discontinuous variates,” Biometrika, vol. 37, no. 1-2, pp. 130–144, 1950. View at Google Scholar · View at Scopus
  20. B. K. Moser, Linear Models: A Mean Model Approach, Academic Press, 1996.
  21. J. Xie, Generalizing the Mann-Whitney-Wilcoxon statistic. [Ph.D. thesis], The Johns Hopkins University, Baltimore, Md, USA, 1999.
  22. M. Kendall and A. Stuart, The Advanced Theory of Statistics, vol. 2, Griffin, UK, 4th edition, 1979.
  23. C. van Eeden, “The relation between Pitman’s asymptotic relative efficiency of two tests and the correlation coefficient between their test statistics,” The Annals of Mathematical Statistics, vol. 34, no. 4, pp. 1442–1451, 1963. View at Google Scholar
  24. P. J. Bickel and A. K. Doksum, Mathematical Statistics, Basic Ideas and Selected Topics, Prentice Hall, Englewood Cliffs, NJ, USA, 1977.
  25. A. Baddeley and R. Turner, “spatstat: an R package for analyzing spatial point patterns,” Journal of Statistical Software, vol. 12, no. 6, pp. 1–42, 2005. View at Google Scholar · View at Scopus
  26. D. J. Gerrard, Competition Quotient: A New Measure of the Competition Affecting Individual Forest Trees, vol. 20 of Research Bulletin, Agricultural Experiment Station, Michigan State University, 1969.
  27. D. Malerba, F. Esposito, and M. Monopoli, “Comparing dissimilarity measures for probabilistic symbolic objects,” Management Information Systems, vol. 6, pp. 31–40, 2002. View at Google Scholar · View at Scopus
  28. M. F. Beg, M. I. Miller, A. Trouvé, and L. Younes, “Computing large deformation metric mappings via geodesic flows of diffeomorphisms,” International Journal of Computer Vision, vol. 61, no. 2, pp. 139–157, 2005. View at Publisher · View at Google Scholar · View at Scopus
  29. R. S. Strichartz, The Way of Analysis, Jones and Bartlett, 2000.