IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v76y2006i14p1503-1509.html
   My bibliography  Save this article

A sufficient condition for the CLT in the space of nuclear operators--Application to covariance of random functions

Author

Listed:
  • Mas, André

Abstract

We give a sufficient condition for the CLT to hold in the space of trace class (nuclear) operators. This condition turns out to be adapted to the asymptotic study of empirical covariance operators of Hilbert valued random variables.

Suggested Citation

  • Mas, André, 2006. "A sufficient condition for the CLT in the space of nuclear operators--Application to covariance of random functions," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1503-1509, August.
    • Handle: RePEc:eee:stapro:v:76:y:2006:i:14:p:1503-1509
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(06)00085-X
    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. Cardot, Hervé & Ferraty, Frédéric & Sarda, Pascal, 1999. "Functional linear model," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 11-22, October.
    2. Mas, André, 2002. "Weak convergence for the covariance operators of a Hilbertian linear process," Stochastic Processes and their Applications, Elsevier, vol. 99(1), pages 117-135, May.
    3. Dauxois, J. & Pousse, A. & Romain, Y., 1982. "Asymptotic theory for the principal component analysis of a vector random function: Some applications to statistical inference," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 136-154, March.
    Full references (including those not matched with items on IDEAS)

    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. Han Shang, 2014. "A survey of functional principal component analysis," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(2), pages 121-142, April.
    2. André Mas, 2002. "Testing for the Mean of Random Curves : from Penalization to Dimension Selection," Working Papers 2002-08, Center for Research in Economics and Statistics.
    3. Qi, Xin & Zhao, Hongyu, 2011. "Some theoretical properties of Silverman's method for Smoothed functional principal component analysis," Journal of Multivariate Analysis, Elsevier, vol. 102(4), pages 741-767, April.
    4. Panaretos, Victor M. & Tavakoli, Shahin, 2013. "Cramér–Karhunen–Loève representation and harmonic principal component analysis of functional time series," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2779-2807.
    5. Julien Jacques & Cristian Preda, 2014. "Functional data clustering: a survey," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(3), pages 231-255, September.
    6. Haolun Shi & Jiguo Cao, 2022. "Robust Functional Principal Component Analysis Based on a New Regression Framework," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(3), pages 523-543, September.
    7. Salish, Nazarii & Gleim, Alexander, 2019. "A moment-based notion of time dependence for functional time series," Journal of Econometrics, Elsevier, vol. 212(2), pages 377-392.
    8. Cardot, Hervé & Johannes, Jan, 2010. "Thresholding projection estimators in functional linear models," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 395-408, February.
    9. Berkes, István & Horváth, Lajos & Rice, Gregory, 2016. "On the asymptotic normality of kernel estimators of the long run covariance of functional time series," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 150-175.
    10. Nie, Yunlong & Cao, Jiguo, 2020. "Sparse functional principal component analysis in a new regression framework," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    11. Kokoszka, Piotr & Reimherr, Matthew, 2013. "Asymptotic normality of the principal components of functional time series," Stochastic Processes and their Applications, Elsevier, vol. 123(5), pages 1546-1562.
    12. Lakraj, Gamage Pemantha & Ruymgaart, Frits, 2017. "Some asymptotic theory for Silverman’s smoothed functional principal components in an abstract Hilbert space," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 122-132.
    13. Cardot, Hervé & Sarda, Pacal, 2005. "Estimation in generalized linear models for functional data via penalized likelihood," Journal of Multivariate Analysis, Elsevier, vol. 92(1), pages 24-41, January.
    14. Hlubinka, Daniel & Prchal, Lubos, 2007. "Changes in atmospheric radiation from the statistical point of view," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4926-4941, June.
    15. repec:eca:wpaper:2013/131191 is not listed on IDEAS
    16. Mingotti, Nicola & Lillo Rodríguez, Rosa Elvira & Romo, Juan, 2015. "A Random Walk Test for Functional Time Series," DES - Working Papers. Statistics and Econometrics. WS ws1506, Universidad Carlos III de Madrid. Departamento de Estadística.
    17. María Edo & Walter Sosa Escudero & Marcela Svarc, 2021. "A multidimensional approach to measuring the middle class," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 19(1), pages 139-162, March.
    18. Guangxing Wang & Sisheng Liu & Fang Han & Chong‐Zhi Di, 2023. "Robust functional principal component analysis via a functional pairwise spatial sign operator," Biometrics, The International Biometric Society, vol. 79(2), pages 1239-1253, June.
    19. Febrero-Bande, Manuel & Galeano, Pedro & González-Manteiga, Wenceslao, 2019. "Estimation, imputation and prediction for the functional linear model with scalar response with responses missing at random," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 91-103.
    20. Ci-Ren Jiang & John A. D. Aston & Jane-Ling Wang, 2016. "A Functional Approach to Deconvolve Dynamic Neuroimaging Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 1-13, March.
    21. Delsol, Laurent & Ferraty, Frédéric & Vieu, Philippe, 2011. "Structural test in regression on functional variables," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 422-447, March.

    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:76:y:2006:i:14:p:1503-1509. 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.