IDEAS home Printed from https://ideas.repec.org/a/bla/jtsera/v27y2006i2p253-287.html
   My bibliography  Save this article

Bernstein polynomial estimation of a spectral density

Author

Listed:
  • Yoshihide Kakizawa

Abstract

. We consider an application of Bernstein polynomials for estimating a spectral density of a stationary process. The resulting estimator can be interpreted as a convex combination of the (Daniell) kernel spectral density estimators at m points, the coefficients of which are probabilities of the binomial distribution bin(m − 1, |λ|/π), λ ∈ Π ≡ [−π, π] being the frequency where the spectral density estimation is made. Several asymptotic properties are investigated under conditions of the degree m. We also discuss methods of data‐driven choice of the degree m. For a comparison with the ordinary kernel method, a Monte Carlo simulation illustrates our methodology and examines its performance in small sample.

Suggested Citation

  • Yoshihide Kakizawa, 2006. "Bernstein polynomial estimation of a spectral density," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(2), pages 253-287, March.
    • Handle: RePEc:bla:jtsera:v:27:y:2006:i:2:p:253-287
    DOI: 10.1111/j.1467-9892.2005.00465.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1467-9892.2005.00465.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1467-9892.2005.00465.x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

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


    Cited by:

    1. Alexandre Leblanc, 2010. "A bias-reduced approach to density estimation using Bernstein polynomials," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(4), pages 459-475.
    2. Alexandre Leblanc, 2009. "Chung–Smirnov property for Bernstein estimators of distribution functions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(2), pages 133-142.
    3. Lu, Lu, 2015. "On the uniform consistency of the Bernstein density estimator," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 52-61.
    4. Bouezmarni, Taoufik & El Ghouch, Anouar & Taamouti, Abderrahim, 2011. "Bernstein estimator for unbounded density copula," UC3M Working papers. Economics we1143, Universidad Carlos III de Madrid. Departamento de Economía.
    5. Kakizawa, Yoshihide, 2007. "Moderate deviations for quadratic forms in Gaussian stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 992-1017, May.
    6. Bouezmarni Taoufik & Ghouch El & Taamouti Abderrahim, 2013. "Bernstein estimator for unbounded copula densities," Statistics & Risk Modeling, De Gruyter, vol. 30(4), pages 343-360, December.
    7. Ouimet, Frédéric, 2021. "Asymptotic properties of Bernstein estimators on the simplex," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    8. BOUEZMARNI, Taoufik & ROMBOUTS, Jeroen V.K. & TAAMOUTI, Abderrahim, 2008. "Asymptotic properties of the Bernstein density copula for dependent data," LIDAM Discussion Papers CORE 2008045, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Bouezmarni, Taoufik & Rombouts, Jeroen V.K. & Taamouti, Abderrahim, 2010. "Asymptotic properties of the Bernstein density copula estimator for [alpha]-mixing data," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 1-10, January.
    10. Brian Hart & Michele Guindani & Stephen Malone & Mark Fiecas, 2022. "A nonparametric Bayesian model for estimating spectral densities of resting‐state EEG twin data," Biometrics, The International Biometric Society, vol. 78(1), pages 313-323, March.

    More about this item

    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:bla:jtsera:v:27:y:2006:i:2:p:253-287. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782 .

    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.