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. 163192. 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 Ustatistics 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: 
19800436 
Publisher: 
Institute of Mathematical Statistics 
Language: 
English 
Submitter: 
David Ginsbourger 
Date Deposited: 
20 Jul 2016 11:00 
Last Modified: 
21 Jul 2016 05:07 
ArXiv ID: 
1502.01568 
BORIS DOI: 
10.7892/boris.84023 
URI: 
https://boris.unibe.ch/id/eprint/84023 