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Original Articles

Spatial Clustering Tests Based on the Domination Number of a New Random Digraph Family

Pages 1363-1395 | Received 29 Jan 2009, Accepted 28 Dec 2009, Published online: 19 Feb 2011

References

  • Baddeley , A. , Møller , J. , Waagepetersen , R. ( 2000 ). Non- and semi-parametric estimation of interaction in inhomogeneous point patterns . Statistica Neerlandica 54 ( 3 ): 329 – 350 .
  • Ceyhan , E. ( 2005 ). An investigation of proximity catch digraphs in delaunay tessellations. Also available as technical monograph titled “Proximity Catch Digraphs: Auxiliary Tools, Properties, and Applications” by VDM Verlag, PhD thesis , The Johns Hopkins University , Baltimore , MD .
  • Ceyhan , E. ( 2008a ). The distribution of the domination number of class cover catch digraphs for non-uniform one-dimensional data . Discrete Mathematics 308 : 5376 – 5393 .
  • Ceyhan , E. ( 2008b ). Overall and pairwise segregation tests based on nearest neighbor contingency tables . Computat. Statist. Data Anal. 53 ( 8 ): 2786 – 2808 .
  • Ceyhan , E. ( 2009a ). Class-specific tests of segregation based on nearest neighbor contingency tables . Statistica Neerlandica 63 ( 2 ): 149 – 182 .
  • Ceyhan , E. ( 2009b ). Spatial clustering tests based on domination number of a new random digraph family. arXiv:0909.3034 [math.ST]. Technical Report # KU-EC-09-6 , Koç University , Istanbul , Turkey .
  • Ceyhan , E. , Priebe , C. ( 2003 ). Central similarity proximity maps in Delaunay tessellations. Proc. Joint Statist. Meeting, Statist. Comput. Sec. Amer. Statist. Assoc. , San Francisco , CA , August 3 – 7 .
  • Ceyhan , E. , Priebe , C. E. ( 2005 ). The use of domination number of a random proximity catch digraph for testing spatial patterns of segregation and association . Statist. Probab. Lett. 73 : 37 – 50 .
  • Ceyhan , E. , Priebe , C. E. ( 2007 ). On the distribution of the domination number of a new family of parametrized random digraphs . Model Assist. Statist. Applic. 1 ( 4 ): 231 – 255 .
  • Ceyhan , E. , Priebe , C. E. , Marchette , D. J. ( 2007 ). A new family of random graphs for testing spatial segregation . Can. J. Statist. 35 ( 1 ): 27 – 50 .
  • Ceyhan , E. , Priebe , C. E. , Wierman , J. C. ( 2006 ). Relative density of the random r-factor proximity catch digraphs for testing spatial patterns of segregation and association . Computat. Statist. Data Anal. 50 ( 8 ): 1925 – 1964 .
  • Chartrand , G. , Lesniak , L. ( 1996 ). Graphs & Digraphs . Boca Raton , FL : Chapman & Hall/CRC Press LLC .
  • Coomes , D. A. , Rees , M. , Turnbull , L. ( 1999 ). Identifying aggregation and association in fully mapped spatial data . Ecology 80 ( 2 ): 554 – 565 .
  • Cuzick , J. , Edwards , R. ( 1990 ). Spatial clustering for inhomogeneous populations (with discussion) . J. Roy. Statist. Soc. Ser. B 52 : 73 – 104 .
  • DeVinney , J. , Priebe , C. E. ( 2006 ). A new family of proximity graphs: Class cover catch digraphs . Discr. Appl. Math. 154 ( 14 ): 1975 – 1982 .
  • DeVinney , J. , Priebe , C. E. , Marchette , D. J. , Socolinsky , D. ( 2002 ). Random walks and catch digraphs in classification . Proc. 34th Symp. Interface: Computing Science and Statistics , Vol. 34 . Available at: http:\\www.galaxy.gmu.edu\interface\I02\I2002 Proceedings\DeVinneyJason\DeVinneyJason.paper.pdf
  • DeVinney , J. , Wierman , J. C. ( 2003 ). A SLLN for a one-dimensional class cover problem . Statist. Probab. Lett. 59 ( 4 ): 425 – 435 .
  • Diggle , P. J. ( 2003 ). Statistical Analysis of Spatial Point Patterns . London : Hodder Arnold Publishers .
  • Dixon , P. M. ( 1994 ). Testing spatial segregation using a nearest-neighbor contingency table . Ecology 75 ( 7 ): 1940 – 1948 .
  • Dixon , P. M. ( 2002a ). Nearest-neighbor contingency table analysis of spatial segregation for several species . Ecoscience 9 ( 2 ): 142 – 151 .
  • Dixon , P. M. (2002b). Nearest neighbor methods. In: El-Shaarawi , A. H. , Piegorsch , W. W. , eds. Encyclopedia of Environmetrics . New York : John Wiley & Sons Ltd. , Vol. 3, pp. 1370–1383.
  • Eeden , C. V. ( 1963 ). The relation between Pitman's asymptotic relative efficiency of two tests and the correlation coefficient between their test statistics . Ann. Mathemat. Statist. 34 ( 4 ): 1442 – 1451 .
  • Fall , A. , Fortin , M. J. , Manseau , M. , O'Brien , D. ( 2007 ). Ecosystems . Int. J. Geograph. Inform. Sci. 10 ( 3 ): 448 – 461 .
  • Friedman , J. H. , Rafsky , L. C. ( 1983 ). Graph-theoretic measures of multivariate association and prediction . Ann. Statist. 11 ( 2 ): 377 – 391 .
  • Good , B. J. , Whipple , S. A. ( 1982 ). Tree spatial patterns: South Carolina bottomland and swamp forests . Bull. Torrey Botanical Club 109 : 529 – 536 .
  • Hodges , J. L. J. , Lehmann , E. L. ( 1956 ). The efficiency of some nonparametric competitors of the t-test . Ann. Mathemat. Statist. 27 ( 2 ): 324 – 335 .
  • Jaromczyk , J. W. , Toussaint , G. T. ( 1992 ). Relative neighborhood graphs and their relatives . Proc. IEEE 80 : 1502 – 1517 .
  • Keitt , T. ( 2007 ). Introduction to spatial modeling with networks. Presented at the Workshop on Networks in Ecology and Beyond Organized by the PRIMES (Program in Interdisciplinary Math, Ecology and Statistics) at Colorado State University, Fort Collins, Colorado .
  • Kendall , M. , Stuart , A. ( 1979 ). The Advanced Theory of Statistics. , 4th ed. Vol. 2 . London : Griffin .
  • Kulldorff , M. ( 2006 ). Tests for spatial randomness adjusted for an inhomogeneity: a general framework . J. Amer. Statist. Assoc. 101 ( 475 ): 1289 – 1305 .
  • Marchette , D. J. , Priebe , C. E. ( 2003 ). Characterizing the scale dimension of a high dimensional classification problem . Pattern Recogn. 36 ( 1 ): 45 – 60 .
  • Minor , E. S. , Urban , D. L. ( 2007 ). Graph theory as a proxy for spatially explicit population models in conservation planning . Ecolog. Applic. 17 ( 6 ): 1771 – 1782 .
  • Okabe , A. , Boots , B. , Sugihara , K. , Chiu , S. N. ( 2000 ). Spatial Tessellations: Concepts and Applications of Voronoi Diagrams . New York : Wiley .
  • Perry , G. , Miller , B. , Enright , N. ( 2006 ). A comparison of methods for the statistical analysis of spatial point patterns in plant ecology . Plant Ecol. 187 ( 1 ): 59 – 82 .
  • Pielou , E. C. ( 1961 ). Segregation and symmetry in two-species populations as studied by nearest-neighbor relationships . J. Ecol. 49 ( 2 ): 255 – 269 .
  • Priebe , C. E. , DeVinney , J. G. , Marchette , D. J. ( 2001 ). On the distribution of the domination number of random class cover catch digraphs . Statist. Probab. Lett. 55 : 239 – 246 .
  • Priebe , C. E. , Marchette , D. J. , DeVinney , J. , Socolinsky , D. ( 2003a ). Classification using class cover catch digraphs . J. Classific. 20 ( 1 ): 3 – 23 .
  • Priebe , C. E. , Solka , J. L. , Marchette , D. J. , Clark , B. T. ( 2003b ). Class cover catch digraphs for latent class discovery in gene expression monitoring by DNA microarrays . Computat. Statist. Data Anal. Visual . 43-4 : 621 – 632 .
  • Ripley , B. D. ( 2004 ). Spatial Statistics . New York : Wiley-Interscience .
  • Roberts , S. A. , Hall , G. B. , Calamai , P. H. ( 2000 ). Analysing forest fragmentation using spatial autocorrelation, graphs and GIS . Int. J. Geograph. Inform. Sci. 14 ( 2 ): 185 – 204 .
  • Stoyan , D. , Penttinen , A. ( 2000 ). Recent applications of point process methods in forestry statistics . Statist. Sci. 15 ( 1 ): 61 – 78 .
  • Su , W. Z. , Yang , G. S. , Yao , S. M. , Yang , Y. B. ( 2007 ). Scale-free structure of town road network in southern Jiangsu Province of China . Chin. Geograph. Sci. 17 ( 4 ): 311 – 316 .
  • Toussaint , G. T. ( 1980 ). The relative neighborhood graph of a finite planar set . Patt. Recogn. 12 ( 4 ): 261 – 268 .
  • West , D. B. (2001). Introduction to Graph Theory. , 2nd ed.Englewood Cliffs , NJ : Prentice Hall.
  • Wierman , J. C. , Xiang , P. ( 2008 ). A general SLLN for the one-dimensional class cover problem . Statist. Probab. Lett. 78 ( 9 ): 1110 – 1118 .
  • Wu , X. , Murray , A. T. ( 2008 ). A new approach to quantifying spatial contiguity using graph theory and spatial interaction . Int. J. Geograph. Inform. Sci. 22 ( 4 ): 387 – 407 .
  • Xiang , P. , Wierman , J. C. ( 2009 ). A CLT for a one-dimensional class cover problem . Statist. Probab. Lett. 79 ( 2 ): 223 – 233 .

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