, Volume 76, Issue 1, pp 19–52 | Cite as

Kernel spatial density estimation in infinite dimension space

  • Sophie Dabo-Niang
  • Anne-Françoise YaoEmail author


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.


Density estimation Random fields Functional variables Infinite dimensional space Small balls probabilities Mixing conditions 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Laboratoire EQUIPPE, University Charles De GaulleVilleneuved’ascq cedexFrance
  2. 2.Laboratoire LMGEM, University Aix-MarseilleMarseille cedex 09France

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