Comportement asymptotique de lʼestimateur non paramétrique de la fonction de renouvellement associée à des variables aléatoires positives indépendantes et non stationnaires

Harel, Michel; Ravelomanantsoa, Fy Mamenosoa

doi:10.1016/j.crma.2013.07.011

Cited by 3 publications

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“…Markovich et al [18] show almost sure convergence of the estimator while Gokpinar et al [19] study consistency, asymptotic unbiasedness and asymptotic normality of the estimator. Harel and Ravelomanantsoa [20] show not only almost sure convergence and asymptotic normality but also weak convergence on Skorohod topology of the estimator. In the two-dimensional and bivariate case, Harel et al [21] study almost sure convergence and asymptotic normality of the estimator while, in the multidimensional and multivariate case, Harel et al [22] prove the weak convergence on Skorohod topology of the estimator.…”

Section: Introductionmentioning

confidence: 99%

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

Andriamampionona,

Harison,

Harel

2024

Mathematics

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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.

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