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math.ST updates on arXiv.org

What is Learnable in Valiant's Theory of the Learnable? 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Nonparametric estimation of the jump rate for non-homogeneous marked renewal processes
Romain Azaïs, François Dufour, Anne Gégout-Petit · 2012-02-10 · via math.ST updates on arXiv.org

This paper is devoted to the nonparametric estimation of the jump rate and the cumulative rate for a general class of non-homogeneous marked renewal processes, defined on a separable metric space. In our framework, the estimation needs only one observation of the process within a long time. Our approach is based on a generalization of the multiplicative intensity model, introduced by Aalen in the seventies. We provide consistent estimators of these two functions, under some assumptions related to the ergodicity of an embedded chain and the characteristics of the process. The paper is illustrated by a numerical example.

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