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On nonparametric conditional quantile estimation for non-stationary spatial processes
Comptes Rendus. Mathématique, Volume 361 (2023), pp. 847-852.

A kernel conditional quantile estimate of a real-valued non-stationary spatial process is proposed for a prediction goal at a non-observed location of the underlying process. The originality is based on the ability to take into account some local spatial dependency. Large sample properties based on almost complete and L q -consistencies of the estimator are established.

Dans cette note, nous présentons un estimateur à noyau du quantile conditionnel d’un processus spatial non-stationnaire, pour un but de prédiction du processus considéré en un site non-observé. L’originalité vient du fait que l’estimateur permet de prendre en compte une éventuelle dépendance locale des données. Une étude asymptotique basée sur les convergences presque complète et en moyenne d’ordre q de l’estimateur est proposée.

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Accepted:
Published online:
DOI: 10.5802/crmath.400
Classification: 62H11, 62G20, 62M30
Serge Hippolyte Arnaud Kanga 1; Ouagnina Hili 1; Sophie Dabo-Niang 2

1 UMRI Mathématiques et Nouvelles Technologies de l’Information, Institut National Polytechnique Félix Houphouët Boigny, BP 1093 Yamoussoukro, Côte d’Ivoire
2 Laboratoire Paul Painlevé UMR CNRS 8524, INRIA-MODAL Université de Lille, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Serge Hippolyte Arnaud Kanga; Ouagnina Hili; Sophie Dabo-Niang. On nonparametric conditional quantile estimation for non-stationary spatial processes. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 847-852. doi : 10.5802/crmath.400. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.400/

[1] Gérard Biau; Benoît Cadre Nonparametric Spatial Prediction, Stat. Inference Stoch. Process., Volume 7 (2004) no. 3, pp. 327-349 | DOI | Zbl

[2] Sophie Dabo-Niang; Leila Hamdad; Camille Ternynck; Anne-Françoise Yao A Kernel Spatial Density Estimation Allowing for the Analysis of Spatial Clustering. Application to Monsoon Asia Drought Atlas data, Stochastic environmental research and risk assessment, Volume 28 (2014) no. 8, pp. 2075-2099 | DOI

[3] Sophie Dabo-Niang; Camille Ternynck; Anne-Françoise Yao Nonparametric Prediction of Spatial Multivariate data, J. Nonparametric Stat., Volume 28 (2016) no. 2, pp. 428-458 | DOI | Zbl

[4] Sophie Dabo-Niang; Baba Thiam Robust Quantile Estimation and Prediction for Spatial Processes, Stat. Probab. Lett., Volume 80 (2010) no. 17-18, pp. 1447-1458 | DOI | Zbl

[5] Sophie Dabo-Niang; Anne-Françoise Yao Kernel Regression Estimation for Continuous Spatial Processes, Math. Methods Stat., Volume 16 (2007) no. 4, pp. 298-317 | DOI | Zbl

[6] Mohamed El Machkouri; Xiequan Fan; Lucas Reding On the Nadaraya–Watson kernel regression estimator for irregularly spaced spatial data, J. Stat. Plann. Inference, Volume 205 (2020), pp. 92-114 | DOI | Zbl

[7] Frédéric Ferraty; Abbes Rabhi; Philippe Vieu Conditional Quantiles for Dependent Functional Data with Application to the Climatic El Niño Phenomenon, Sankhyā, Volume 67 (2005) no. 2, pp. 378-398 | Zbl

[8] Marc Hallin; Zudi Lu; Keming Yu Local Linear Spatial Quantile Regression, Bernoulli, Volume 15 (2009) no. 3, pp. 659-686 | Zbl

[9] Meiling Huang; Christine Nguyen A Nonparametric Approch for Quantile Regression, J. Stat. Distrib. Appl., Volume 5 (2018), 3 | Zbl

[10] Jussi Klemelä Density Estimation with Locally Identically Distributed Data and with Locally Stationary Data, J. Time Ser. Anal., Volume 29 (2008) no. 1, pp. 125-141 | Zbl

[11] Roger Koenker; Ivan Mizera Penalized Triograms: Total Variation Regularization for Bivariate Smoothing, J. R. Stat. Soc., Ser. B, Stat. Methodol., Volume 66 (2004) no. 1, pp. 145-164 | DOI | Zbl

[12] S. A. Ould Abdi; Sophie Dabo-Niang; Aliou Diop; A. Ould Abdi Consistency of a Nonparametric Conditional Quantile Estimator for Random Fields, Math. Methods Stat., Volume 19 (2010) no. 1, pp. 1-21 | DOI | Zbl

[13] Camille Ternynck Contributions à la Modélisation de Données Spatiales et Fonctionnelles: Applications, Ph. D. Thesis, Université Charles de Gaulle-Lille III, Lille, France (2014)

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