Nonparametric prediction of spatial multivariate data

References

• Allard, D., D'Or, D., and Froidevaux, R. (2011), ‘An Efficient Maximum Entropy Approach for Categorical Variable Prediction’, European Journal of Soil Science, 62, 381–393. doi: 10.1111/j.1365-2389.2011.01362.x
   Web of Science ®Google Scholar
• Atteia, O., Dubois, J.P., and Webster, R. (1994), ‘Geostatistical Analysis of Soil Contamination in the Swiss Jura’, Environmental Pollution, 86, 315–327. doi: 10.1016/0269-7491(94)90172-4
   PubMed Web of Science ®Google Scholar
• Atteia, O., Thélin, P., Pfeifer, H.R., Dubois, J.P., and Hunziker, J.C. (1995), ‘A Search for the Origin of Cadmium in the Soil of the Swiss Jura’, Geoderma, 68, 149–172. doi: 10.1016/0016-7061(95)00037-O
   Web of Science ®Google Scholar
• Bel, L., Allard, D., Laurent, J.M., Cheddadi, R., and Bar-Hen, A. (2009), ‘CART Algorithm for Spatial Data: Application to Environmental and Ecological Data’, Comput. Statist. Data Anal., 53, 3082–3093. doi: 10.1016/j.csda.2008.09.012
   Web of Science ®Google Scholar
• Biau, G., and Cadre, B. (2004), ‘Nonparametric Spatial Prediction’, Statistical Inference for Stochastic Process, 7, 327–349. doi: 10.1023/B:SISP.0000049116.23705.88
   Google Scholar
• Bosq, D. (1998), Nonparametric Statistics for Stochastic Processes: Estimation and Prediction (2nd ed.), Volume 110 of Lecture Notes in Statistics, New York: Springer.
   Google Scholar
• Carbon, M., Francq, C., and Tran, L.T. (2007), ‘Kernel Regression Estimation for Random Fields’, Journal of Statistics Planning Inference, 137, 778–798. doi: 10.1016/j.jspi.2006.06.008
   Web of Science ®Google Scholar
• Carbon, M., Tran, L.T., and Wu, B. (1997), ‘Kernel Density Estimation for Random Fields (density estimation for random fields)’, Statistics & Probability Letters, 36, 115–125. doi: 10.1016/S0167-7152(97)00054-0
   Web of Science ®Google Scholar
• Chamizo, L.F., and Iwaniec, H. (1995), ‘On the Sphere Problem’, Revista Matemàtica Iberoamericana, 11, 417–430. doi: 10.4171/RMI/178
   Web of Science ®Google Scholar
• Cressie, N.A.C. (1993), N.A.C.: Statistics for Spatial Data (revised ed.), Vol. 110 of Wiley Series on Probability Statistics, New York: Wiley-Interscience.
   Google Scholar
• Dabo-Niang, S., Hamdad, L., Ternynck, C., and Yao, A.F. (2014), ‘A Kernel Spatial Density Estimation Allowing for the Analysis of Spatial Clustering: Application to Monsoon Asia Drought Atlas Data’, Stochastic Environmental Research Risk Assessment, 28, 2075–2099. doi: 10.1007/s00477-014-0903-6
   Web of Science ®Google Scholar
• Dabo-Niang, S., and Yao, A.F. (2007), ‘Kernel Regression Estimation for Continuous Spatial Processes’, Mathematical Methods of Statistics, 16, 298–317. doi: 10.3103/S1066530707040023
   Google Scholar
• El Machkouri, M. (2007), ‘Nonparametric Regression Estimation for Random Fields in a Fixed-Design’, Statistical Inference for Stochastic Processes, 10, 29–47. doi: 10.1007/s11203-005-7332-6
   Google Scholar
• El Machkouri, M. (2011), ‘Asymptotic Normality of the Parzen–Rosenblatt Density Estimator for Strongly Mixing Random Fields’, Statistical Inference for Stochastic Processes, 14, 73–84. doi: 10.1007/s11203-011-9052-4
   Google Scholar
• El Machkouri, M., and Stoica, R. (2010), ‘Asymptotic Normality of Kernel Estimates in a Regression Model for Random Fields’, Journal of Nonparametric Statistics, 22, 955–971. doi: 10.1080/10485250903505893
   Web of Science ®Google Scholar
• Francisco-Fernández, M., and Opsomer, J.D. (2005), ‘Smoothing Parameter Selection Methods for Nonparametric Regression with Spatially Correlated Errors’, Canadian Journal of Statistics, 33, 279–295. doi: 10.1002/cjs.5550330208
   Web of Science ®Google Scholar
• Francisco-Fernández, M., Quintela-del Río, A., and Fernández-Casal, R. (2012), ‘Nonparametric Methods for Spatial Regression. An Application to Seismic Events’, Environmetrics, 23, 85–93. doi: 10.1002/env.1146
   Web of Science ®Google Scholar
• Gaetan, C., and Guyon, X. (2008), Modélisation et statistique spatiales, Vol. 63, Berlin: Springer-Verlag.
   Google Scholar
• Goovaerts, P. (1997), Geostatistics for Natural Resources Evaluation, New York: Oxford University Press.
   Google Scholar
• Goovaerts, P. (1998), ‘Ordinary Cokriging Revisited’, Mathematical Geology, 30, 21–42. doi: 10.1023/A:1021757104135
   Google Scholar
• Kelejian, H.H., and Prucha, I.R. (2007), ‘HAC Estimation in a Spatial Framework’, Journal of Econometrics, 140, 131–154. doi: 10.1016/j.jeconom.2006.09.005
   Web of Science ®Google Scholar
• Klemelä, J. (2008), ‘Density Estimation with Locally Identically Distributed Data and with Locally Stationary Data’, Journal of Time Series Analysis, 29, 125–141.
   Web of Science ®Google Scholar
• Masry, E. (2005), ‘Nonparametric Regression Estimation for Dependent Functional Data: Asymptotic Normality’, Stochastic Processes and their Application, 115, 155–177. doi: 10.1016/j.spa.2004.07.006
   Web of Science ®Google Scholar
• Menezes, R., García-Soidán, P., and Ferreira, C. (2010), ‘Nonparametric Spatial Prediction under Stochastic Sampling Design’, Journal of Nonparametric Statistics, 22, 363–377. doi: 10.1080/10485250903094294
   Web of Science ®Google Scholar
• Meyer, A. (2011), ‘On the number of lattice points in a small sphere,’ in WCC 2011 – Workshop on Coding and Cryptography, pp. 463–472.
   Google Scholar
• Mitchell, W.C. (1966), ‘The Number of Lattice Points in a k-Dimensional Hypersphere’, Mathematics of Computation, 20, 300–310.
   Web of Science ®Google Scholar
• Neaderhouser, C.C. (1980), ‘Convergence of Block Spins Defined by a Random Field’, Journal of Statistical Physics, 22, 673–684. doi: 10.1007/BF01013936
   Web of Science ®Google Scholar
• Rosenblatt, M. (1985), Stationary Sequences and Random Fields, Boston, MA: Birkhauser.
   Google Scholar
• Takahata, H. (1983), ‘On the Rates in the Central Limit Theorem for Weakly Dependent Random Fields’, Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 64, 445–456. doi: 10.1007/BF00534950
   Web of Science ®Google Scholar
• Ternynck, C. (2014), ‘Spatial Regression Estimation for Functional Data with Spatial Dependency’, Journal de la Société Française de Statistique, 155, 138–160.
   Google Scholar
• Tran, L.T. (1990), ‘Kernel Density Estimation on Random Fields’, Journal of Multivariate Analysis, 34, 37–53. doi: 10.1016/0047-259X(90)90059-Q
   Web of Science ®Google Scholar
• Tsang, K.M. (2000), ‘Counting Lattice Points in the Sphere’, Bulletin London Mathematical Society, 32, 679–688. doi: 10.1112/S0024609300007505
   Web of Science ®Google Scholar
• Wackernagel, H. (2003), Multivariate Geostatistics: An Introduction with Applications (3rd ed.), Berlin: Springer-Verlag.
   Google Scholar
• Wang, H., Wang, J., and Huang, B. (2012), ‘Prediction for Spatio-temporal Models with Autoregression in Errors’, Journal of Nonparametric Statistics, 24, 217–244. doi: 10.1080/10485252.2011.616893
   Web of Science ®Google Scholar
• Webster, R., Atteia, O., and Dubois, J.P. (1994), ‘Coregionalization of Trace Metals in the Soil in the Swiss Jura’, European Journal of Soil Science, 45, 205–218. doi: 10.1111/j.1365-2389.1994.tb00502.x
   Web of Science ®Google Scholar