Statistical Inference for Stochastic Processes, volume 25, issue 3, pages 485-504
Weak convergence of nonparametric estimators of the multidimensional and multidimensional-multivariate renewal functions on Skorohod topology spaces
Michel Harel
1, 2
,
Joseph Ngatchou-Wandji
3
,
Livasoa Andriamampionona
4
,
Victor Harison
4
2
INSPE de Limoges, Université de Limoges, Limoges Cedex, France
|
3
EHESP Rennes & Institut Élie Cartan de Lorraine, Vandoeuvre-lès-Nancy Cedex, France
|
Publication type: Journal Article
Publication date: 2021-11-29
scimago Q3
SJR: 0.363
CiteScore: 1.3
Impact factor: 0.7
ISSN: 13870874, 15729311
Statistics and Probability
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.
Found
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