RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Probl. Peredachi Inf.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Probl. Peredachi Inf., 2018, Volume 54, Issue 4, Pages 60–81 (Mi ppi2281)  

Methods of Signal Processing

Noise level estimation in high-dimensional linear models

G. K. Golubevab, E. A. Krymovabc

a CNRS, Aix-Marseille Université, I2M, Marseille, France
b Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia
c Duisburg-Essen University, Duisburg, Germany

Abstract: We consider the problem of estimating the noise level $\sigma^2$ in a Gaussian linear model $Y=X\beta+\sigma \xi$, where $\xi\in\mathbb{R}^n$ is a standard discrete white Gaussian noise and $\beta\in\mathbb{R}^p$ an unknown nuisance vector. It is assumed that $X$ is a known ill-conditioned $n\times p$ matrix with $n\ge p$ and with large dimension $p$. In this situation the vector $\beta$ is estimated with the help of spectral regularization of the maximum likelihood estimate, and the noise level estimate is computed with the help of adaptive (i.e., data-driven) normalization of the quadratic prediction error. For this estimate, we compute its concentration rate around the pseudo-estimate $\|Y-X\beta\|^2/n$.

Funding Agency Grant Number
Deutsche Forschungsgemeinschaft SFB 823
Russian Foundation for Basic Research 15-07-09121_а
Supported in part by the Russian Foundation for Basic Research, project no. 15-07-09121, and the German Research Foundation (DFG), project SFB 823: Statistical Modelling of Nonlinear Dynamic Processes.


Full text: PDF file (274 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Problems of Information Transmission, 2018, 54:4, 351–371

Bibliographic databases:

UDC: 621.391.1:519.2
Received: 23.08.2017
Revised: 09.08.2018
Accepted:13.11.2018

Citation: G. K. Golubev, E. A. Krymova, “Noise level estimation in high-dimensional linear models”, Probl. Peredachi Inf., 54:4 (2018), 60–81; Problems Inform. Transmission, 54:4 (2018), 351–371

Citation in format AMSBIB
\Bibitem{GolKry18}
\by G.~K.~Golubev, E.~A.~Krymova
\paper Noise level estimation in high-dimensional linear models
\jour Probl. Peredachi Inf.
\yr 2018
\vol 54
\issue 4
\pages 60--81
\mathnet{http://mi.mathnet.ru/ppi2281}
\elib{http://elibrary.ru/item.asp?id=38647189}
\transl
\jour Problems Inform. Transmission
\yr 2018
\vol 54
\issue 4
\pages 351--371
\crossref{https://doi.org/10.1134/S003294601804004X}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000456991400004}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85060762689}


Linking options:
  • http://mi.mathnet.ru/eng/ppi2281
  • http://mi.mathnet.ru/eng/ppi/v54/i4/p60

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Проблемы передачи информации Problems of Information Transmission
    Number of views:
    This page:50
    References:9
    First page:2

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019