On rate of convergence in non-central limit theorems

Anh, Vo, Leonenko, Nikolai N. ORCID: https://orcid.org/0000-0003-1932-4091, Olenko, Andriy and Vaskovych, Volodymyr 2019. On rate of convergence in non-central limit theorems. Bernoulli 25 (4A) , pp. 2920-2948. 10.3150/18-BEJ1075

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Abstract

The main result of this paper is the rate of convergence to Hermite-type distributions in non-central limit theorems. To the best of our knowledge, this is the first result in the literature on rates of convergence of functionals of random fields to Hermite-type distributions with ranks greater than 2. The results were obtained under rather general assumptions on the spectral densities of random fields. These assumptions are even weaker than in the known convergence results for the case of Rosenblatt distributions. Additionally, Lévy concentration functions for Hermite-type distributions were investigated.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	Bernoulli Society for Mathematical Statistics and Probability
ISSN:	1350-7265
Related URLs:	Publisher
Date of First Compliant Deposit:	18 September 2018
Date of Acceptance:	17 September 2018
Last Modified:	19 Nov 2024 03:45
URI:	https://orca.cardiff.ac.uk/id/eprint/115083

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