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Kernel spatial density estimation in infinite dimension space

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Abstract

In this paper, we propose a nonparametric method to estimate the spatial density of a functional stationary random field. This latter is with values in some infinite dimensional normed space and admitted a density with respect to some reference measure. We study both the weak and strong consistencies of the considered estimator and also give some rates of convergence. Special attention is paid to the links between the probabilities of small balls and the rates of convergence of the estimator. The practical use and the behavior of the estimator are illustrated through some simulations and a real data application.

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Authors and Affiliations

  1. Laboratoire EQUIPPE, University Charles De Gaulle, Lille 3 maison dela recherche, domaine du pont de bois, BP 60149, 59653, Villeneuved’ascq cedex, France

    Sophie Dabo-Niang

  2. Laboratoire LMGEM, University Aix-Marseille, Campus de Luminy, case 901, 13288, Marseille cedex 09, France

    Anne-Françoise Yao

Authors
  1. Sophie Dabo-Niang
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  2. Anne-Françoise Yao
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Correspondence to Anne-Françoise Yao.

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Dabo-Niang, S., Yao, AF. Kernel spatial density estimation in infinite dimension space. Metrika 76, 19–52 (2013). https://doi.org/10.1007/s00184-011-0374-4

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  • DOI: https://doi.org/10.1007/s00184-011-0374-4

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