Weak convergence of nonparametric estimators of the multidimensional and multidimensional-multivariate renewal functions on Skorohod topology spaces. (English) Zbl 1497.60125
Summary: 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.
MSC:
| 60K05 | Renewal theory |
| 60F17 | Functional limit theorems; invariance principles |
| 62E20 | Asymptotic distribution theory in statistics |
| 62G05 | Nonparametric estimation |
| 62G20 | Asymptotic properties of nonparametric inference |
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