IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v80y2010i23-24p1724-1732.html
   My bibliography  Save this article

Relation between unit operators proximity and their associated spectral measures

Author

Listed:
  • Boudou, Alain
  • Viguier-Pla, Sylvie

Abstract

In this paper, we study how the local concentration of the spectral measure can be expressed in the temporal domain for stationary processes. For this purpose, we establish an equivalence between the proximity of the shift operators (which are unit operators) and the associated projector valued spectral measures. An illustration is given.

Suggested Citation

  • Boudou, Alain & Viguier-Pla, Sylvie, 2010. "Relation between unit operators proximity and their associated spectral measures," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1724-1732, December.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:23-24:p:1724-1732
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(10)00210-5
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Boudou, Alain & Romain, Yves, 2002. "On spectral and random measures associated to discrete and continuous-time processes," Statistics & Probability Letters, Elsevier, vol. 59(2), pages 145-157, September.
    2. Dominique Dehay & Vincent Monsan, 2007. "Discrete Periodic Sampling with Jitter and Almost Periodically Correlated Processes," Statistical Inference for Stochastic Processes, Springer, vol. 10(3), pages 223-253, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Boudou, Alain & Viguier-Pla, Sylvie, 2016. "Gap between orthogonal projectors—Application to stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 282-300.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Boudou, Alain & Romain, Yves, 2010. "On the integral with respect to the tensor product of two random measures," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 385-394, February.
    2. Boudou, Alain & Viguier-Pla, Sylvie, 2022. "Principal components analysis and cyclostationarity," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    3. Boudou, Alain & Viguier-Pla, Sylvie, 2016. "Gap between orthogonal projectors—Application to stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 282-300.
    4. Alain, Boudou & Sylvie, Viguier-Pla, 2014. "Structure of the random measure associated with an isotropic stationary process," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 111-128.
    5. Aneiros, Germán & Cao, Ricardo & Fraiman, Ricardo & Genest, Christian & Vieu, Philippe, 2019. "Recent advances in functional data analysis and high-dimensional statistics," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 3-9.
    6. Boudou, A. & Cabral, E.N. & Romain, Y., 2010. "Centered and non-centered principal component analyses in the frequency domain," Statistics & Probability Letters, Elsevier, vol. 80(2), pages 96-103, January.
    7. Giuseppe Cavaliere & Dimitris N. Politis & Anders Rahbek & Dominique Dehay & Anna E. Dudek, 2015. "Recent developments in bootstrap methods for dependent data," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(3), pages 327-351, May.
    8. Boudou, Alain & Viguier-Pla, Sylvie, 2019. "Commuter of operators in a Hilbert space," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 244-262.

    More about this item

    Keywords

    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:80:y:2010:i:23-24:p:1724-1732. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.