A kernel spatial density estimation allowing for the analysis of spatial clustering. Application to Monsoon Asia Drought Atlas data |
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Authors: | Sophie Dabo-Niang Leila Hamdad Camille Ternynck Anne-Françoise Yao |
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Institution: | 1. Laboratoire EQUIPPE, Université Charles De Gaulle, Lille 3, Villeneuve-d’Ascq, France 2. MODAL team, INRIA Lille-Nord de France, Lille, France 3. Laboratoire LCSI, école Nationale Supérieure d’Informatique, El Harrach, Algéria 4. Laboratoire de Mathématiques, Université Blaise Pascal, UMR 6620 - CNRS Campus des Cézeaux, 63171, Aubière cedex, France
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Abstract: | A nonparametric density estimate that incorporates spatial dependency has not been studied in the literature. In this article, we propose a new spatial density estimator that depends on two kernels: one controls the distance between observations while the other controls the spatial dependence structure. The uniform almost sure convergence of the density estimate is established with the rate of convergence. The consistency of the mode of this kernel density is also studied. Then a spatial hierarchical unsupervised clustering algorithm based on the mode estimate is presented. Some simulations as well as an application to the Monsoon Asia Drought Atlas data illustrate the efficiency of our algorithm, and a comparison of the spatial structures of these data detected by the density estimate and clustering algorithm are done. |
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