Recovery of periodicities hidden in heavy†tailed noise

Illya M. Karabash and Jürgen Prestin

Mathematische Nachrichten, 2018, vol. 291, issue 1, 86-102

Abstract: We address a parametric joint detection†estimation problem for discrete signals of the form x(t)=∑n=1Nαne−iλnt+εt, t∈N, with an additive noise represented by independent centered complex random variables εt. The distributions of εt are assumed to be unknown, but satisfying various sets of conditions. We prove that in the case of a heavy†tailed noise it is possible to construct asymptotically strongly consistent estimators for the unknown parameters of the signal, i.e., frequencies λn, their number N, and complex coefficients αn. For example, one of considered classes of noise is the following: εt are independent identically distributed random variables with E(εt)=0 and E(|εt|ln|εt|)

Date: 2018
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.201600361

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:291:y:2018:i:1:p:86-102

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0025-584X

Access Statistics for this article

Mathematische Nachrichten is currently edited by Robert Denk

More articles in Mathematische Nachrichten from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().