Resample-smoothing of Voronoi intensity estimators

Statistics and Computing - Tập 29 Số 5 - Trang 995-1010 - 2019
Mehdi Moradi1, Ottmar Cronie2, Ege Rubak3, Raphaël Lachièze-Rey4, Jorge Mateu5, Adrian Baddeley6
1Institute of New Imaging Technologies (INIT), University Jaume I, Castellón, Spain
2Umeå University
3Aalborg University, Denmark
4Mathématiques Appliquées Paris 5
5Department of Mathematics, University Jaume I, Castellón, Spain
6School of Mathematics and Statistics [Crawley, Perth]

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Ang, Q.W., Baddeley, A., Nair, G.: Geometrically corrected second order analysis of events on a linear network, with applications to ecology and criminology. Scand. J. Stat. 39(4), 591–617 (2012)

Baddeley, A.: Validation of statistical models for spatial point patterns. In: Babu, J., Feigelson, E. (eds) Statistical Challenges in Modern Astronomy IV, Astronomical Society of the Pacific, San Francisco, California, USA, Astronomical Society of the Pacific, Conference Series, vol. 371, pp. 22–38 (2007)

Baddeley, A., Rubak, E., Turner, R.: Spatial Point Patterns: Methodology and Applications with R. CRC Press, Boca Raton (2015)

Barr, C.D., Schoenberg, F.P.: On the Voronoi estimator for the intensity of an inhomogeneous planar Poisson process. Biometrika 97(4), 977–984 (2010)

Berman, M., Diggle, P.: Estimating weighted integrals of the second-order intensity of a spatial point process. J. R. Stat. Soc. Ser. B 51, 81–92 (1989)

Borruso, G.: Network density estimation: analysis of point patterns over a network. In: Computational Science and Its Applications—ICCSA 2005, Springer, pp. 126–132 (2005)

Borruso, G.: Network density and the delimitation of urban areas. Trans. GIS 7, 177–191 (2003)

Borruso, G.: Network density estimation: a GIS approach for analysing point patterns in a network space. Trans. GIS 12(3), 377–402 (2008)

Brown, G.S.: Point density in stems per acre. Forest Research Institute, New Zealand Forest Service (1965)

Chiu, S.N., Stoyan, D., Kendall, W.S., Mecke, J.: Stochastic Geometry and Its Applications. Wiley, Hoboken (2013)

Cronie, O., Särkkä, A.: Some edge correction methods for marked spatio-temporal point process models. Comput. Stat. Data Anal. 55(7), 2209–2220 (2011)

Cronie, O., van Lieshout, M.N.M.: A non-model-based approach to bandwidth selection for kernel estimators of spatial intensity functions. Biometrika 105(2), 455–462 (2018)

Daley, D.J., Vere-Jones, D.: An Introduction to the Theory of Point Processes: Volume II: General Theory and Structure, 2nd edn. Springer, New York (2008)

Davies, T.M., Baddeley, A.: Fast computation of spatially adaptive kernel estimates. Stat. Comput. 28(4), 937–956 (2018)

Davies, T.M., Hazelton, M.L.: Adaptive kernel estimation of spatial relative risk. Stat. Med. 29(23), 2423–2437 (2010)

Davies, T.M., Jones, K., Hazelton, M.L.: Symmetric adaptive smoothing regimens for estimation of the spatial relative risk function. Comput. Stat. Data Anal. 101, 12–28 (2016)

Davies, T.M., Marshall, J.C., Hazelton, M.L.: Tutorial on kernel estimation of continuous spatial and spatiotemporal relative risk. Stat. Med. 37(7), 1191–1221 (2018)

Diggle, P.: A kernel method for smoothing point process data. Appl. Stat. 34(2), 138–147 (1985)

Diggle, P.: Statistical Analysis of Spatial and Spatio-Temporal Point Patterns, 3rd edn. CRC Press, Boca Raton (2014)

Duyckaerts, C., Godefroy, G.: Voronoi tessellation to study the numerical density and the spatial distribution of neurones. J. Chem. Neuroanat. 20(1), 83–92 (2000)

Duyckaerts, C., Godefroy, G., Hauw, J.J.: Evaluation of neuronal numerical density by Dirichlet tessellation. J. Neurosci. Methods 51(1), 47–69 (1994)

Ebeling, H., Wiedenmann, G.: Detecting structure in two dimensions combining Voronoi tessellation and percolation. Phys. Rev. E 47(1), 704–710 (1993)

Ferreira, J., Denison, D., Holmes, C.: Partition modelling. In: Lawson, A., Denison, D. (eds.) Spatial Cluster Modelling, chap 7, pp. 125–146. CRC Press, Boca Raton (2002)

Heikkinen, J., Arjas, E.: Non-parametric Bayesian estimation of a spatial Poisson intensity. Scand. J. Stat. 25(3), 435–450 (1998)

Holmström, L., Hamalainen, A.: The self-organizing reduced kernel density estimator. In: IEEE International Conference on Neural Networks, pp. 417–421 (1993)

Kallenberg, O.: Random Measures, Theory and Applications. Springer, Berlin (2017)

Last, G.: Stationary random measures on homogeneous spaces. J. Theor. Probab. 23(2), 478–497 (2010)

Lawrence, T., Baddeley, A., Milne, R.K., Nair, G.: Point pattern analysis on a region of a sphere. Stat 5(1), 144–157 (2016)

Levine, N.: Houston, Texas, metropolitan traffic safety planning program. Transp. Res. Record J. Transp. Res. Board 1969, 92–100 (2006)

Levine, N.: A motor vehicle safety planning support system: the Houston experience. In: Geertman, S., Stillwell, J. (eds.) Planning Support Systems Best Practice and New Methods, pp. 93–111. Springer, Dordrecht (2009)

Loader, C.: Local Regression and Likelihood. Springer, New York (1999)

McSwiggan, G., Baddeley, A., Nair, G.: Kernel density estimation on a linear network. Scand. J. Stat. 44(2), 324–345 (2017)

Møller, J., Rubak, E.: Functional summary statistics for point processes on the sphere with an application to determinantal point processes. Spat. Stat. 18, 4–23 (2016)

Møller, J., Schoenberg, F.: Thinning spatial point processes into Poisson processes. Adv. Appl. Probab. 42(2), 347–358 (2010)

Moradi, M.M., Rodríguez-Cortés, F.J., Mateu, J.: On the intensity estimator of spatial point patterns on linear networks. J. Comput. Graph. Stat. 27(2), 302–311 (2018)

Ogata, Y.: Significant improvements of the space-time etas model for forecasting of accurate baseline seismicity. Earth Planets Space 63(3), 217–229 (2011)

Okabe, A., Sugihara, K.: Spatial Analysis Along Networks: Statistical and Computational Methods. Wiley, Hoboken (2012)

Okabe, A., Boots, B., Sugihara, K., Chiu, S.: Spatial Tessellations: Concepts and Applications of Voronoi Diagrams, 2nd edn. Wiley, Hoboken (2000)

Okabe, A., Satoh, T., Sugihara, K.: A kernel density estimation method for networks, its computational method and a gis-based tool. Int. J. Geogr. Inf. Sci. 23(1), 7–32 (2009)

Ord, J.: How many trees in a forest? Math. Sci. 3, 23–33 (1978)

Rakshit, S., Davies, T.M., Moradi, M.M., McSwiggan, G., Nair, G., Mateu, J., Baddeley, A.: Fast kernel smoothing of point patterns on a large network using 2D convolution. Submitted for publication (2018)

Rakshit, S., Nair, G., Baddeley, A.: Second-order analysis of point patterns on a network using any distance metric. Spat. Stat. 22, 129–154 (2017)

Schaap, W.E.: DTFE: the Delaunay tessellation field estimator. PhD thesis, University of Groningen (2007)

Schneider, R., Weil, W.: Stochastic and Integral Geometry. Probability and Its Applications. Springer, Dordrecht (2008)

Scott, D.: Multivariate Density Estimation. Theory, Practice and Visualization. Wiley, New York (1992)

Silverman, B.W.: Density Estimation for Statistics and Data Analysis. CRC Press, Boca Raton (1986)

van Lieshout, M.N.M.: Markov Point Processes and Their Applications. Imperial College Press, London (2000)

van Lieshout, M.N.M.: On estimation of the intensity function of a point process. Methodol. Comput. Appl. Probab. 14, 567–578 (2012)

Wand, M., Jones, M.: Kernel Smoothing. CRC Press, Boca Raton (1995)

Xie, Z., Yan, J.: Kernel density estimation of traffic accidents in a network space. Comput. Environ. Urb. Syst. 32(5), 396–406 (2008)