Towards an Interval-Valued Estimation of the Density

Bilal Nehme 1 Olivier Strauss 2
2 ICAR - Image & Interaction
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : This paper presents a theoretical and practical novel approach for computing the probability density function underlying a set of observations. The estimator we propose is an extension of the conventional Parzen Rosenblatt method that leads to a very specific interval-valued estimation of the density. Within this approach, we make use of the convenient representation of a set of usual (summative) kernels by a maxitive kernel (i.e. a possibility distribution) to derive an exact computation with a very low complexity of an interval-valued estimation. The considered set of kernels is particularly convenient since it contains kernels having comparable shapes and bandwidth. We prove that the obtained imprecise probability density function contains a set of precise density functions estimated using the standard method with kernels belonging to the considered set.
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Bilal Nehme, Olivier Strauss. Towards an Interval-Valued Estimation of the Density. WCCI: World Congress on Computational Intelligence, 2010, Barcelona, Spain. pp.3114-3119. ⟨lirmm-00505969⟩

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