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A new spatial regression estimator in the multivariate context

Sophie Dabo-Niang 1 Anne-Françoise Yao 2 Camille Ternynck 3
1 MODAL - MOdel for Data Analysis and Learning
Inria Lille - Nord Europe, LPP - Laboratoire Paul Painlevé - UMR 8524, METRICS - Evaluation des technologies de santé et des pratiques médicales - ULR 2694, Polytech Lille - École polytechnique universitaire de Lille, Université de Lille, Sciences et Technologies
2 Equipe Probabilités, Analyse et Statistique
LMBP - Laboratoire de Mathématiques Blaise Pascal
Abstract : In this note, we propose a nonparametric spatial estimator of the regression function View the MathML sourcex→r(x):=E[Yi|Xi=x],x∈Rd, of a stationary (d+1)(d+1)-dimensional spatial process View the MathML source{(Yi,Xi),i∈ZN}, at a point located at some station j. The proposed estimator depends on two kernels in order to control both the distance between observations and the spatial locations. Almost complete convergence and consistency in LqLq norm (q∈N⁎)(q∈N⁎) of the kernel estimate are obtained when the sample considered is an α-mixing sequence.
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Submitted on : Tuesday, September 29, 2015 - 3:55:39 PM
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Sophie Dabo-Niang, Anne-Françoise Yao, Camille Ternynck. A new spatial regression estimator in the multivariate context. Comptes rendus de l'Académie des sciences. Série I, Mathématique, Elsevier, 2015, 353 (7), pp.635 - 639. ⟨10.1016/j.crma.2015.04.004⟩. ⟨hal-01206781⟩



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