IDEAS home Printed from https://ideas.repec.org/p/mcm/deptwp/2015-03.html
   My bibliography  Save this paper

Information Measures for Nonparametric Kernel Estimation

Author

Listed:
  • Neshat Beheshti
  • Jeffrey S. Racine
  • Ehsan S. Soofi

Abstract

This paper addresses the following question: How much information do the kernel function and the bandwidth provide for nonparametric kernel estimation? The question is addressed by showing that kernel estimation of a cumulative distribution function (CDF) is an information transmission procedure for transforming the empirical cumulative distribution function into a smooth estimate. The transmission channel is the kernel function itself, which is a conditional distribution with a data point as its location parameter and a bandwidth as its scale parameter. The output of the information transmission procedure is the kernel estimate of the CDF which is a marginal distribution constructed as the sample average of the kernel functions centered at each data point. This framework provides a lower bound for the entropy of the kernel estimate of the distribution in terms of the entropy of the kernel function and the bandwidth, an input information measure for kernel smoothing, and a measure of information for kernel estimation. A family of maximum entropy kernels that includes several well-known kernel functions is identified. These kernels are compared according to the information measures developed herein.

Suggested Citation

  • Neshat Beheshti & Jeffrey S. Racine & Ehsan S. Soofi, 2015. "Information Measures for Nonparametric Kernel Estimation," Department of Economics Working Papers 2015-03, McMaster University.
    • Handle: RePEc:mcm:deptwp:2015-03
    as

    Download full text from publisher

    File URL: http://socserv.mcmaster.ca/econ/rsrch/papers/archive/2015-03.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Clive Granger & Jin‐Lung Lin, 1994. "Using The Mutual Information Coefficient To Identify Lags In Nonlinear Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(4), pages 371-384, July.
    2. C. W. Granger & E. Maasoumi & J. Racine, 2004. "A Dependence Metric for Possibly Nonlinear Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(5), pages 649-669, September.
    3. P. M. Robinson, 1991. "Consistent Nonparametric Entropy-Based Testing," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(3), pages 437-453.
    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. Asadi, Majid & Ebrahimi, Nader & Soofi, Ehsan S. & Zohrevand, Younes, 2016. "Jensen–Shannon information of the coherent system lifetime," Reliability Engineering and System Safety, Elsevier, vol. 156(C), pages 244-255.

    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. Matilla-García, Mariano & Marín, Manuel Ruiz, 2010. "A new test for chaos and determinism based on symbolic dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 76(3), pages 600-614, December.
    2. Luca Bagnato & Lucio De Capitani & Antonio Punzo, 2014. "Testing Serial Independence via Density-Based Measures of Divergence," Methodology and Computing in Applied Probability, Springer, vol. 16(3), pages 627-641, September.
    3. Matilla-Garci­a, Mariano & Ruiz Mari­n, Manuel, 2008. "A non-parametric independence test using permutation entropy," Journal of Econometrics, Elsevier, vol. 144(1), pages 139-155, May.
    4. Henry Lam, 2018. "Sensitivity to Serial Dependency of Input Processes: A Robust Approach," Management Science, INFORMS, vol. 64(3), pages 1311-1327, March.
    5. repec:wyi:journl:002087 is not listed on IDEAS
    6. Dionisio, Andreia & Menezes, Rui & Mendes, Diana & Vidigal Da Silva, Jacinto, 2007. "Nonlinear Dynamics Within Macroeconomic Factors And Stock Market In Portugal, 1993-2003," Applied Econometrics and International Development, Euro-American Association of Economic Development, vol. 7(2), pages 57-70.
    7. Andreia Dionisio & Rui Menezes & Diana A. Mendes & Jacinto Vidigal da Silva, 2004. "Linear and nonlinear models for the analysis of the relationship between stock market prices and macroeconomic and financial factors," Econometrics 0411018, University Library of Munich, Germany.
    8. Hong, Yongmiao, 2001. "A test for volatility spillover with application to exchange rates," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 183-224, July.
    9. Esfandiar Maasoumi & Jeffrey Racine, 2009. "A Robust Entropy-Based Test of Asymmetry for Discrete and Continuous Processes," Econometric Reviews, Taylor & Francis Journals, vol. 28(1-3), pages 246-261.
    10. Yongmiao Hong & Xia Wang & Wenjie Zhang & Shouyang Wang, 2017. "An efficient integrated nonparametric entropy estimator of serial dependence," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 728-780, October.
    11. Cees Diks & Sebastiano Manzan, 2001. "Tests for Serial Independence and Linearity based on Correlation Integrals," Tinbergen Institute Discussion Papers 01-085/1, Tinbergen Institute.
    12. Wu, Ximing, 2010. "Exponential Series Estimator of multivariate densities," Journal of Econometrics, Elsevier, vol. 156(2), pages 354-366, June.
    13. Arthur Lewbel, 2000. "Asymptotic Trimming for Bounded Density Plug-in Estimators," Boston College Working Papers in Economics 479, Boston College Department of Economics, revised 30 Oct 2000.
    14. Diks Cees & Panchenko Valentyn, 2008. "Rank-based Entropy Tests for Serial Independence," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(1), pages 1-21, March.
    15. Cees Diks & Valentyn Panchenko, 2005. "Nonparametric Tests for Serial Independence Based on Quadratic Forms," Tinbergen Institute Discussion Papers 05-076/1, Tinbergen Institute.
    16. L. Bagnato & L. De Capitani & A. Punzo, 2016. "The Kullback–Leibler autodependogram," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(14), pages 2574-2594, October.
    17. Yoon, Gawon, 2010. "Do real exchange rates really follow threshold autoregressive or exponential smooth transition autoregressive models?," Economic Modelling, Elsevier, vol. 27(2), pages 605-612, March.
    18. Menezes, Rui & Dionísio, Andreia & Hassani, Hossein, 2012. "On the globalization of stock markets: An application of Vector Error Correction Model, Mutual Information and Singular Spectrum Analysis to the G7 countries," The Quarterly Review of Economics and Finance, Elsevier, vol. 52(4), pages 369-384.
    19. Yongmiao Hong, 2013. "Serial Correlation and Serial Dependence," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    20. Matilla-García, Mariano & Ruiz Marín, Manuel, 2009. "Detection of non-linear structure in time series," Economics Letters, Elsevier, vol. 105(1), pages 1-6, October.
    21. Heather M. Anderson, 2002. "Choosing Lag Lengths in Nonlinear Dynamic Models," Monash Econometrics and Business Statistics Working Papers 21/02, Monash University, Department of Econometrics and Business Statistics.

    More about this item

    Keywords

    information diagnostics; Kernel selection; entropy; mutual information.;
    All these keywords.

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:mcm:deptwp:2015-03. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/demcmca.html .

    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.