A Monte Carlo-Adjusted Goodness-of-Fit Test for Parametric Models Describing Spatial Point Patterns

REFERENCES

• Assunção, R.M. (1994), “Testing Spatial Randomness by Means of Angles,” Biometrics, 50, 531–537.
   Google Scholar
• Assunção, R.M., and Reis, I.A. (2000), “Testing Spatial Randomness: A Comparison Between T2 Methods and Modifications of the Angle Test,” Brazilian Journal of Probability and Statistics, 14, 71–86.
   Google Scholar
• Baddeley, A.J., Møller, J., and Pakes, A.G. (2008), “Properties of Residuals for Spatial Point Processes,” Annals of the Institute of Statistical Mathematics, 60, 629–649.
   Google Scholar
• Baddeley, A.J., Møller, J., and Waagepetersen, R.P. (2000), “Non- and Semi-Parametric Estimation of Interaction in Inhomogeneous Point Patterns,” Statistica Neerlandica, 54, 329–350.
   Web of Science ®Google Scholar
• Baddeley, A.J., and Turner, R. (2000), “Practical Maximum Pseudolikelihood for Spatial Point Patterns,” Australian & New Zealand Journal of Statistics, 42, 283–322.
   Web of Science ®Google Scholar
• ——— (2005), “Spatstat: An R Package for Analyzing Spatial Point Patterns,” Journal of Statistical Software, 12, 1–42.
   Web of Science ®Google Scholar
• Baddeley, A.J., Turner, R., Møller, J., and Hazelton, M. (2005), “Residual Analysis for Spatial Point Processes” (with discussion), Journal of the Royal Statistical Society, Series B, 67, 617–666.
   Google Scholar
• Bartlett, M.S. (1964), “The Spectral Analysis of Point Processes,” Biometrika, 51, 299–311.
   Web of Science ®Google Scholar
• Bayarri, M.J., and Berger, J.O. (2000), “P Values in Composite Null Models,” Journal of the American Statistical Association, 95, 1127–1142.
   Web of Science ®Google Scholar
• Berman, M., and Turner, T.R. (1992), “Approximating Point Process Likelihoods With GLIM,” Applied Statistics, 41, 31–38.
   Web of Science ®Google Scholar
• Besag, J.E. (1978), “Some Methods of Statistical Analysis of Spatial Data,” Bulletin of the International Statistical Institute, 47, 77–92.
   Google Scholar
• Besag, J.E., and Clifford, P. (1991), “Sequential Monte Carlo p-Values,” Biometrika, 78, 301–304.
   Web of Science ®Google Scholar
• Besag, J.E., and Diggle, P.J. (1977), “Simple Monte Carlo Tests for Spatial Patterns,” Applied Statistics, 26, 327–333.
   Google Scholar
• Besag, J.E., and Gleaves, J.T. (1973), “On the Detection of Spatial Pattern in Plant Communities,” Bulletin of the International Statistical Institute, 45, 153–158.
   Google Scholar
• Cressie, N. A.C. (1993), Statistics for Spatial Data (revised ed.), New York: Wiley.
   Google Scholar
• Diggle, P.J. (2003), Statistical Analysis of Spatial Point Patterns (2nd ed.), London: Arnold.
   Google Scholar
• Diggle, P.J., and Gratton, R.J. (1984), “Monte Carlo Methods of Inference for Implicit Statistical Models” (with discussion), Journal of the Royal Statistical Society, Series B, 46, 193–227.
   Google Scholar
• Donnelly, K. (1978), “Simulations to Determine the Variance and Edge-Effect of Total Nearest Neighbor Distance,” in Simulation Methods in Archaeology, ed. I. Hoddler, London: Cambridge University Press, pp. 91–95.
   Google Scholar
• Guan, Y. (2008), “A Goodness-of-Fit Test for Inhomogeneous Spatial Poisson Processes,” Biometrika, 95, 831–845.
   Google Scholar
• Hines, W. G.S., and Hines, R. J.O. (1979), “The Eberhardt Index and the Detection of Non-randomness of Spatial Point Distributions,” Biometrika, 66, 73–80.
   Google Scholar
• Huang, F., and Ogata, Y. (1999), “Improvements of the Maximum Pseudo-Likelihood Estimators in Various Spatial Statistical Models,” Journal of Computational and Graphical Statistics, 8, 510–530.
   Web of Science ®Google Scholar
• Illian, J., Penttinen, A., Stoyan, H., and Stoyan, D. (2008), Statistical Analysis and Modelling of Spatial Point Patterns (Statistics in Practice), West Sussex, England: Wiley.
   Google Scholar
• Illian, J.B., Møller, J., and Waagepetersen, R.P. (2009), “Hierarchical Spatial Point Process Analysis for a Plant Community With High Biodiversity,” Environmental and Ecological Statistics, 16, 389–405.
   Google Scholar
• Marriott, F. H.C. (1979), “Monte Carlo Tests: How Many Simulations,” Applied Statistics, 28, 75–77.
   Google Scholar
• Møller, J., and Waagepetersen, R.P. (2003), Statistical Inference and Simulation for Spatial Point Processes, London: Chapman and Hall/CRC Press.
   Google Scholar
• R Development Core Team (2012), R: A Language and Environment for Statistical Computing, Vienna, Austria: R Foundation for Statistical Computing.
   Google Scholar
• Ripley, B.D. (1977), “Modelling Spatial Patterns” (with discussion), Journal of the Royal Statistical Society, Series B, 39, 172–212.
   Google Scholar
• ——— (1988), Statistical Inference for Spatial Processes, Australia: Cambridge University Press.
   Google Scholar
• Robins, J.M., Van der Vaart, A., and Ventura, V. (2000), “Asymptotic Distribution of P Values in Composite Null Models,” Journal of the American Statistical Association, 95, 1143–1156.
   Web of Science ®Google Scholar