Non-Parametric Estimation of the Renewal Function for Multidimensional Random Fields

Livasoa Andriamampionona (), Victor Harison and Michel Harel
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Livasoa Andriamampionona: Department of Mathematics and Informatics, University of Antananarivo, Antananarivo 101, Madagascar
Victor Harison: Department of Mathematics and Informatics, University of Antananarivo, Antananarivo 101, Madagascar
Michel Harel: Laboratoire Vie-Santé, UR 24 134, Faculté de Médecine, 2 Av. Martin Luther King, 87025 Limoges, France

Mathematics, 2024, vol. 12, issue 12, 1-22

Abstract: This paper addresses the almost sure convergence and the asymptotic normality of an estimator of the multidimensional renewal function based on random fields. The estimator is based on a sequence of non-negative independent and identically distributed ( i . i . d . ) multidimensional random fields and is expressed as infinite sums of k -folds convolutions of the empirical distribution function. It is an extension of the work from the case of the two-dimensional random fields to the case of the d -dimensional random fields where d > 2 . This is established by the definition of a “strict order relation”. Concrete applications are given.

Keywords: renewal function; almost sure convergence; asymptotic normality; random fields (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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