Fissler, Tobias; Thäle, Christoph (2016). A four moments theorem for Gamma limits on a Poisson chaos. Alea. Latin American journal of probability and mathematical statistics, 13(1), pp. 163-192. Institute of Mathematical Statistics
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This paper deals with sequences of random variables belonging to a
fixed chaos of order q generated by a Poisson random measure on a Polish space. The problem is investigated whether convergence of the third and fourth moment of such a suitably normalized sequence to the third and fourth moment of a centred Gamma law implies convergence in distribution of the involved random variables. A positive answer is obtained for q = 2 and q = 4. The proof of this four moments theorem is based on a number of new estimates for contraction norms. Applications concern homogeneous sums and U-statistics on the Poisson space.
Item Type: |
Journal Article (Original Article) |
|---|---|
Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science |
UniBE Contributor: |
Fissler, Tobias |
Subjects: |
500 Science > 510 Mathematics |
ISSN: |
1980-0436 |
Publisher: |
Institute of Mathematical Statistics |
Language: |
English |
Submitter: |
David Ginsbourger |
Date Deposited: |
20 Jul 2016 11:00 |
Last Modified: |
05 Dec 2022 14:57 |
ArXiv ID: |
1502.01568 |
BORIS DOI: |
10.7892/boris.84023 |
URI: |
https://boris.unibe.ch/id/eprint/84023 |
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