IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v101y2010i2p385-394.html
   My bibliography  Save this article

On the integral with respect to the tensor product of two random measures

Author

Listed:
  • Boudou, Alain
  • Romain, Yves

Abstract

A Fubini-type formula for the integral with respect to the tensor product of two random measures is established in an intrinsic way. This permits one to consider a convolution product. The results are applied to a stationary continuous random function (which may be multiplicatively written with two stationary components) and to principal component analysis in the frequency domain.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:jmvana:v:101:y:2010:i:2:p:385-394
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(09)00059-1
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Boudou, A. & Dauxois, J., 1994. "Principal Component Analysis for a Stationary Random Function Defined on a Locally Compact Abelian Group," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 1-16, October.
    2. 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.
    3. Dehay, Dominique, 1991. "On the product of two harmonizable time series," Stochastic Processes and their Applications, Elsevier, vol. 38(2), pages 347-358, August.
    4. Rosenberg, Milton, 1974. "Operators as spectral integrals of operator-valued functions from the study of multivariate stationary stochastic processes," Journal of Multivariate Analysis, Elsevier, vol. 4(2), pages 166-209, June.
    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. 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.

    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, 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.
    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, 2010. "Relation between unit operators proximity and their associated spectral measures," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1724-1732, December.
    4. 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.
    5. 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.
    6. Jason Hong Jae Park, 2019. "Random Measure Algebras Under O-dot Product and Morse-Transue Integral Convolution," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 8(6), pages 1-73, November.
    7. 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.
    8. Ombao, Hernando & Ringo Ho, Moon-ho, 2006. "Time-dependent frequency domain principal components analysis of multichannel non-stationary signals," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2339-2360, May.
    9. 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.
    10. Aneiros, Germán & Horová, Ivana & Hušková, Marie & Vieu, Philippe, 2022. "On functional data analysis and related topics," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    11. Jolliffe, Ian, 2022. "A 50-year personal journey through time with principal component analysis," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    12. Boudou, Alain, 2006. "Approximation of the principal components analysis of a stationary function," Statistics & Probability Letters, Elsevier, vol. 76(6), pages 571-578, March.
    13. Boudou, Alain & Viguier-Pla, Sylvie, 2019. "Commuter of operators in a Hilbert space," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 244-262.

    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:jmvana:v:101:y:2010:i:2:p:385-394. 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.