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kernel estimation; marked Poisson process; mean mark estimation; location-dependent mark distribution; segment process
We discuss the prediction of a spatial variable of a multivariate mark composed of both dependent and explanatory variables. The marks are location-dependent and they are attached to a point process. We assume that the marks are assigned independently, conditionally on an unknown underlying parametric field. We compare (i) the classical non-parametric Nadaraya-Watson kernel estimator based on the dependent variable (ii) estimators obtained under an assumption of local parametric model where explanatory variables of the local model are estimated through kernel estimation and (iii) a kernel estimator of the result of the parametric model, supposed here to be a Uniformly Minimum Variance Unbiased Estimator derived under the local parametric model when complete and sufficient statistics are available. The comparison is done asymptotically and by simulations in special cases. The procedure for better estimator selection is then illustrated on a real-life data set.
[1] Bouchon, J., Faille, Lemée, G., Robin, A. M., Schmitt, A.: Cartes et notice des sols, du peuplement forestier et des groupements végétaux de la réserve biologique de la Tillaie en forêt de Fontainebleau. University of Orsay 1973.
[2] Coudun, C., Gegout, J. C.: Quantitative prediction of the distribution and abundance of Vaccinium myrtillus (L.) with climatic and edaphic factors. J. Vegetation Sci. 18 (2007), 4, 517-524. DOI 10.1111/j.1654-1103.2007.tb02566.x
[3] Finney, D. J.: On the distribution of a variable whose logarithm is normally distributed. J. Roy. Statist. Soc. Ser. B 7 (1941), 155-161. MR 0006649
[4] Flénet, F., Villon, P., Ruget, F.: Methodology of adaptation of the STICS model to a new crop: spring linseed (Linum usitatissimum, L.). Agronomie 24 (2004), 6-7, 367-381. MR 2108558
[5] Green, W. H.: Econometric Analysis. Prentice Hall, New Jersey 2003.
[6] Guinier, Ph.: Foresterie et protection de la nature. L'exemple de Fontainebleau. Rev. Forestière Française II (1950), 703-717.
[7] Härdle, W.: Applied Non-parametric Regression. Cambridge University Press, Cambridge 1990.
[8] Illian, J., Penttinen, A., Stoyan, H., Stoyan, D.: Statistical Analysis and Modelling of Spatial Point Patterns. Wiley, New York 2008. MR 2384630 | Zbl 1197.62135
[9] Kelsall, J., Diggle, P. J.: Kernel estimation of relative risk. Bernoulli 1 (1995), 3-16. DOI 10.2307/3318678 | MR 1354453 | Zbl 0830.62039
[10] Kelsall, J., Diggle, P. J.: Non-parametric estimation of spatial variation in relative risk. Statist. Medicine 14 (1995), 2335-2342. DOI 10.1002/sim.4780142106
[11] Lawson, A. B.: Statistical Methods in Spatial Epidemiology. Wiley, Chichester 2001. MR 1852711 | Zbl 1096.62118
[12] Lehmann, E. L.: Theory of Point Estimation. Wadsworth & Brooks, California 1991. MR 1143059 | Zbl 0916.62017
[13] Mrkvička, T.: Estimation variances for Poisson process of compact sets. Adv. Appl. Prob. (SGSA) 33 (2001), 765-772. DOI 10.1239/aap/1011994028 | MR 1875778
[14] Mrkvička, T.: Estimation variances for parameterized marked point processes and for parameterized Poisson segment processes. Comment. Math. Univ. Carolin. 45,1 (2004), 109-117. MR 2076863
[15] Mrkvička, T.: Estimation of intersection intensity in Poisson processes of segments. Comment. Math. Univ. Carolin. 48 (2007), 93-106. MR 2338832
[16] Mrkvička, T., Soubeyrand, S., Chadoeuf, J.: Goodness-of-fit Test of the Mark Distribution in a Point Process with Non-stationary Marks. Research Report 36, Biostatistics and Spatial Processes Research Unit. INRA, Avignon 2009.
[17] Noblet-Ducoudré, N. de, Gervois, S., Ciais, P., Viovy, N., Brisson, N., Seguin, B., Perrier, A.: Coupling the soil-vegetation-atmosphere-transfer scheme ORCHIDEE to the agronomy model STICS to study the influence of croplands on the european carbon and water budgets. Agronomie 24 (2004), 6-7, 397-407.
[18] Penttinen, A., Stoyan, D., Hentonnen, H.: Marked point processes in forests statistics. Forest Sci. 38 (1992), 4, 806-824.
[19] Pontailler, J. Y., Faille, A., Lemee, G.: Storms drive successiinal dynamics in natural forests: a case study in Fontainebleau forest (France). Forest Ecology and Management 98 (1997), 1-15.
[20] Silverman, B. W.: Density Estimation for Statistics and Data Analysis. Chapman and Hall, London 1986. MR 0848134 | Zbl 0617.62042
[21] Stoyan, D., Kendall, W. S., Mecke, J.: Stochastic Geometry and Its Applications. Second edition. John Wiley and Sons, New York 1995. MR 0895588
[22] Bodegom, P. Van, Verburg, P. H., Stein, A., Adiningsih, S., Gon, H. A. C. Denier Van Der: Effects of interpolation and data resolution on methane emission estimates from rice paddies. Environ. Ecol. Statist. 9 (2002), 5-26. DOI 10.1023/A:1013755405957 | MR 1881785
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