Poissonization Principle for a Class of Additive Statistics Full article
| Journal |
Mathematics
, E-ISSN: 2227-7390 |
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| Output data | Year: 2022, Volume: 10, Number: 21, Article number : 4084, Pages count : DOI: 10.3390/math10214084 | ||||
| Tags | additive functional; empirical point process; group frequency; Poisson point process; Poissonization | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Russian Science Foundation | 22-21-00414 |
Abstract:
In this paper, we consider a class of additive functionals of a finite or countable collection of the group frequencies of an empirical point process that corresponds to, at most, a countable partition of the sample space. Under broad conditions, it is shown that the asymptotic behavior of the distributions of such functionals is similar to the behavior of the distributions of the same functionals of the accompanying Poisson point process. However, the Poisson versions of the additive functionals under consideration, unlike the original ones, have the structure of sums (finite or infinite) of independent random variables that allows us to reduce the asymptotic analysis of the distributions of additive functionals of an empirical point process to classical problems of the theory of summation of independent random variables. © 2022 by the authors.
Cite:
Borisov I.
, Jetpisbaev M.
Poissonization Principle for a Class of Additive Statistics
Mathematics. 2022. V.10. N21. 4084 . DOI: 10.3390/math10214084 WOS Scopus РИНЦ OpenAlex
Poissonization Principle for a Class of Additive Statistics
Mathematics. 2022. V.10. N21. 4084 . DOI: 10.3390/math10214084 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Sep 5, 2022 |
| Accepted: | Oct 29, 2022 |
| Published print: | Nov 2, 2022 |
| Published online: | Nov 2, 2022 |
Identifiers:
| Web of science: | WOS:000884545700001 |
| Scopus: | 2-s2.0-85141876805 |
| Elibrary: | 57508806 |
| OpenAlex: | W4309090453 |