Weak convergence of nonparametric estimators of the multidimensional and multidimensional-multivariate renewal functions on Skorohod topology spaces

Michel Harel (), Joseph Ngatchou-Wandji (), Livasoa Andriamampionona and Victor Harison ()
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Michel Harel: Institut de Mathématiques de Toulouse
Joseph Ngatchou-Wandji: EHESP Rennes & Institut Élie Cartan de Lorraine
Livasoa Andriamampionona: University of Antananarivo
Victor Harison: University of Antananarivo

Statistical Inference for Stochastic Processes, 2022, vol. 25, issue 3, No 4, 485-504

Abstract: Abstract This paper deals with the weak convergence of nonparametric estimators of the multidimensional and multidimensional-multivariate renewal functions on Skorohod topology spaces. It is an extension of Harel et al. (J Math Anal Appl 189:240–255, 1995) from the one-dimensional case to the multivariate and multidimensional case. The estimators are based on a sequence of non-negative independent and identically distributed (iid) random vectors. They are expressed as infinite sums of k-folds convolutions of the empirical distribution function. Their weak convergence study heavily rests on that of the empirical distribution function.

Keywords: Renewal function; Renewal process; Skorohod topology; Weak convergence; Primary 60F05; 60F17; Secondary 62M86; 62G20 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s11203-021-09263-3

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