A second order approach to analyse spatial point patterns with functional marks

• Comas C, Palahi M, Pukkala T, Mateu J (2009) Characterising forest spatial structures through inhomogeneous second order characteristics. Stoch Environ Res Risk Assess 23:387–397

  Article  MathSciNet  Google Scholar 

• Daley DJ, Vere-Jones D (2004) An introduction to the theory of point processes, 2nd edn. Springer, New York

  Google Scholar 

• Diggle PJ (1975) Robust density estimation using distance methods. Biometrika 62:39–48

  Article  MathSciNet  MATH  Google Scholar 

• Diggle PJ (2003) Statistical analysis of spatial point patterns. Hodder Arnold, Sevenoaks

  MATH  Google Scholar 

• Ferraty F, Vieu P (2006) Nonparametric functional data analysis. Theory and practice. Springer series in statistics. Springer, New York

  MATH  Google Scholar 

• Giraldo R, Delicado P, Mateu J (2009) Continuous time-varying kriging for spatial prediction of functional data: an environmental application. J Agric Biol Environ Statist (JABES) 15(1):66–82

  Article  MathSciNet  Google Scholar 

• Giraldo R, Delicado P, Mateu J (2010) Geostatistics for functional data: an ordinary kriging approach. Environ Ecol Stat. doi:10.1007/s10651-010-0143-y

• Glass L, Tobler WR (1971) Uniform distribution of objects in a homogeneous field: cities on a plain. Nature 233:67–68

  Article  Google Scholar 

• Illian J, Benson E, Crowford J, Staines H (2005) Principal component analysis for spatial point processes-assessing the appropriateness of the approach in an ecological context. In: Baddeley A, Gregori P, Mateu J, Stoica R, Stoyan D (eds) Case studies in spatial point process modeling. Lecture notes in statistics, vol 185. Springer, Berlin

  Google Scholar 

• Illian J, Penttinen A, Stoyan H, Stoyan D (2008) Statistical analysis and modelling of spatial point patterns. Wiley, New York

  MATH  Google Scholar 

• Isham V (1987) Marked point processes and their correlations. In: Droesbeke F (ed) Spatial processes and spatial time series analysis, proceedings of the 6th Franco-Belgian meeting of statisticians, 1985. Publications des Facultés Universitaires Saint-Louis, Brussels, pp 63–75

  Google Scholar 

• Lewis SM (1975) Robust estimation of density for a two-dimensional point process. Biometrika 62:519–521

  Article  MathSciNet  MATH  Google Scholar 

• Mateu J, Usó JL, Montes F (1998) The spatial pattern of forest ecosystems. Ecol Model 108:163–174

  Article  Google Scholar 

• Mateu J, Lorenzo G, Porcu E (2008) Detecting features in spatial point processes with clutter via local indicators of spatial association. J Comput Graph Stat 16:968–990

  MathSciNet  Google Scholar 

• Morisita M (1957) A new method for the estimation of density by spacing method applicable to non-randomly distributed populations. Physiol Ecol 7:134–144

  Google Scholar 

• Patil SA, Burnham KP, Kovner JL (1982) Optimum non-parametric estimation of population density based on ordered distance. Biometrics 38:243–248

  Article  MATH  Google Scholar 

• Penttinen A, Stoyan D (1989) Statistical analysis for a class of line segment processes. Scand J Stat 16:153–161

  MathSciNet  MATH  Google Scholar 

• Penttinen A, Stoyan D, Henttonen HM (1992) Marked point processes in forest statistics. Forest Sci 38:806–824

  Google Scholar 

• Ramsay J, Silverman B (2001) Functional data analysis. In: International encyclopedia of social and behavioral sciences. Elsevier, Amsterdam, pp 5822–5828

  Chapter  Google Scholar 

• Ramsay J, Silverman B (2005) Functional data analysis, 2nd edn. Springer, New York

  Google Scholar 

• Renshaw E, Särkkä A (2001) Gibbs point processes for studying the development of spatial-temporal stochastic processes. Comput Stat Data Anal 36:85–105

  Article  MATH  Google Scholar 

• Renshaw E, Mateu J, Saura F (2007) Disentangling mark/point interaction in marked point processes. Comput Stat Data Anal 51:3123–3144

  Article  MathSciNet  MATH  Google Scholar 

• Ripley BD (1976) The second-order analysis of stationary point processes. J Appl Probab 13:255–266

  Article  MathSciNet  MATH  Google Scholar 

• Ripley BD (1988) Statistical inference for spatial processes. Cambridge University Press, Cambridge

  Google Scholar 

• Särkkä A (1992) A note on robust intensity estimation for point processes. Biom J 34:757–767

  Article  Google Scholar 

• Schlather M (2001) On the second-order characteristics of marked point processes. Bernoulli 7:99–117

  Article  MathSciNet  MATH  Google Scholar 

• Schlather M, Ribeiro PJ, Diggle PJ (2004) Detecting dependence between marks and locations of marked point processes. J R Stat Soc B 66:79–93

  Article  MathSciNet  MATH  Google Scholar 

• Stoyan D (1984) On correlations of marked point processes. Math Nachr 116:197–207

  Article  MathSciNet  MATH  Google Scholar 

• Stoyan D, Stoyan H (1994) Fractals, random shapes and point fields: methods of geometrical statistics. Wiley, Chichester

  MATH  Google Scholar 

• Stoyan D, Kendall WS, Mecke J (1995) Stochastic geometry and its applications. Wiley, New York

  MATH  Google Scholar 

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