On a Szegö type limit theorem, the Hölder-Young-Brascamp-Lieb inequality, and the asymptotic theory of integrals and quadratic forms of stationary fields

Avram, Florin, Leonenko, Nikolai N. ORCID: https://orcid.org/0000-0003-1932-4091 and Sakhno, Ludmila 2010. On a Szegö type limit theorem, the Hölder-Young-Brascamp-Lieb inequality, and the asymptotic theory of integrals and quadratic forms of stationary fields. ESAIM: Probability and Statistics 14 , pp. 210-255. 10.1051/ps:2008031

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Abstract

Many statistical applications require establishing central limit theorems for sums/integrals or for quadratic forms , where X t is a stationary process. A particularly important case is that of Appell polynomials h(X t ) = P m (X t ), h(X t ,X s ) = P m , n (X t ,X s ), since the “Appell expansion rank" determines typically the type of central limit theorem satisfied by the functionals S T (h), Q T (h). We review and extend here to multidimensional indices, along lines conjectured in [F. Avram and M.S. Taqqu, Lect. Notes Statist. 187 (2006) 259–286], a functional analysis approach to this problem proposed by [Avram and Brown, Proc. Amer. Math. Soc. 107 (1989) 687–695] based on the method of cumulants and on integrability assumptions in the spectral domain; several applications are presented as well.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Uncontrolled Keywords:	Quadratic forms; Appell polynomials; Hölder-Young inequality; Szegö type limit theorem; asymptotic normality; minimum contrast estimation
Additional Information:	Pdf uploaded in accordance with publisher's policy at http://www.sherpa.ac.uk/romeo/issn/1292-8100/ (accessed 25/02/2014).
Publisher:	Cambridge University Press
ISSN:	1292-8100
Date of First Compliant Deposit:	30 March 2016
Last Modified:	16 May 2023 05:10
URI:	https://orca.cardiff.ac.uk/id/eprint/13899

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