IDEAS home Printed from https://ideas.repec.org/p/zbw/kondp2/344.html
   My bibliography  Save this paper

A bootstrap bandwidth selector for local polynomial fitting

Author

Listed:
  • Heiler, Siegfried
  • Feng, Yuanhua

Abstract

A bandwidth selector for local polynomial fitting is proposed following the bootstrap idea, which is just a double smoothing bandwidth selector with a bootstrap variance estimator, defined as the mean squared residuals of a pilot estimate. No simulated resampling is required in this context, since the needed expressions can be calculated explicitly. A simple, iterative data-driven procedure is proposed to estimate the variance and the bandwidth. A simulation study shows that this bandwidth selector performs very well, and it performs uniformly better than a double smoothing bandwidth selector using a difference-based variance estimator. The above mentioned bootstrap variance estimator is also a side result of this paper. It performs clearly better than the difference-based one. In a test example, the averaged squared error of this estimator in 500 replications achieved the theoretical lower bound already with a sample size of only n = 200.

Suggested Citation

  • Heiler, Siegfried & Feng, Yuanhua, 1997. "A bootstrap bandwidth selector for local polynomial fitting," Discussion Papers, Series II 344, University of Konstanz, Collaborative Research Centre (SFB) 178 "Internationalization of the Economy".
    • Handle: RePEc:zbw:kondp2:344
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/101542/1/733234372.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Cao, R., 1993. "Bootstrapping the Mean Integrated Squared Error," Journal of Multivariate Analysis, Elsevier, vol. 45(1), pages 137-160, April.
    2. Heiler, Siegfried & Feng, Yuanhua, 1995. "A simple root n bandwidth selector for nonparametric regression," Discussion Papers, Series II 286, University of Konstanz, Collaborative Research Centre (SFB) 178 "Internationalization of the Economy".
    3. HÄRDLE, Wolfgang & HALL, Peter & MARRON, Steve, 1992. "Regression smoothing parameters that are not far from their optimum," LIDAM Reprints CORE 978, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Cao, Ricardo & Cuevas, Antonio & Gonzalez Manteiga, Wensceslao, 1994. "A comparative study of several smoothing methods in density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 17(2), pages 153-176, February.
    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. Heiler, Siegfried, 1999. "A Survey on Nonparametric Time Series Analysis," CoFE Discussion Papers 99/05, University of Konstanz, Center of Finance and Econometrics (CoFE).
    2. Yuanhua Feng, 2013. "Double-conditional smoothing of high-frequency volatility surface in a spatial multiplicative component GARCH with random effects," Working Papers CIE 65, Paderborn University, CIE Center for International Economics.
    3. K. Żychaluk, 2014. "Bootstrap bandwidth selection method for local linear estimator in exponential family models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(2), pages 305-319, June.
    4. Yuanhua Feng, 2013. "An iterative plug-in algorithm for decomposing seasonal time series using the Berlin Method," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(2), pages 266-281, February.
    5. Yuanhua Feng & Thomas Gries, 2017. "Data-driven local polynomial for the trend and its derivatives in economic time series," Working Papers CIE 102, Paderborn University, CIE Center for International Economics.

    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. Barbeito, Inés & Cao, Ricardo, 2016. "Smoothed stationary bootstrap bandwidth selection for density estimation with dependent data," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 130-147.
    2. García-Portugués, Eduardo & Crujeiras, Rosa M. & González-Manteiga, Wenceslao, 2013. "Kernel density estimation for directional–linear data," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 152-175.
    3. Heiler, Siegfried & Feng, Yuanhua, 1995. "A simple root n bandwidth selector for nonparametric regression," Discussion Papers, Series II 286, University of Konstanz, Collaborative Research Centre (SFB) 178 "Internationalization of the Economy".
    4. J. M. Vilar & R. Cao & M. C. Ausin & C. Gonzalez-Fragueiro, 2009. "Nonparametric analysis of aggregate loss models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(2), pages 149-166.
    5. Maria Jácome & Ricardo Cao, 2008. "Asymptotic-based bandwidth selection for the presmoothed density estimator with censored data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(6), pages 483-506.
    6. Isabel Fuentes-Santos & Wenceslao González-Manteiga & Jorge Mateu, 2016. "Consistent Smooth Bootstrap Kernel Intensity Estimation for Inhomogeneous Spatial Poisson Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 416-435, June.
    7. Nils-Bastian Heidenreich & Anja Schindler & Stefan Sperlich, 2013. "Bandwidth selection for kernel density estimation: a review of fully automatic selectors," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(4), pages 403-433, October.
    8. Bose, Arup & Dutta, Santanu, 2013. "Density estimation using bootstrap bandwidth selector," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 245-256.
    9. Jin Zhang, 2015. "Generalized least squares cross-validation in kernel density estimation," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(3), pages 315-328, August.
    10. Ichimura, Hidehiko & Todd, Petra E., 2007. "Implementing Nonparametric and Semiparametric Estimators," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 74, Elsevier.
    11. Chacón, José E. & Fernández Serrano, Javier, 2024. "Bayesian taut splines for estimating the number of modes," Computational Statistics & Data Analysis, Elsevier, vol. 196(C).
    12. Beran, Jan & Feng, Yuanhua, 2000. "Data-driven estimation of semiparametric fractional autoregressive models," CoFE Discussion Papers 00/16, University of Konstanz, Center of Finance and Econometrics (CoFE).
    13. Beran, Jan & Feng, Yuanhua, 2002. "Recent Developments in Non- and Semiparametric Regression with Fractional Time Series Errors," CoFE Discussion Papers 02/13, University of Konstanz, Center of Finance and Econometrics (CoFE).
    14. Adriano Z. Zambom & Ronaldo Dias, 2013. "A Review of Kernel Density Estimation with Applications to Econometrics," International Econometric Review (IER), Econometric Research Association, vol. 5(1), pages 20-42, April.
    15. Yuanhua Feng & Jan Beran, 2013. "Optimal convergence rates in non-parametric regression with fractional time series errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(1), pages 30-39, January.
    16. Matthew A. Masten & Alexandre Poirier, 2020. "Inference on breakdown frontiers," Quantitative Economics, Econometric Society, vol. 11(1), pages 41-111, January.
    17. del Rio, Alejandro Quintela, 1996. "Comparison of bandwidth selectors in nonparametric regression under dependence," Computational Statistics & Data Analysis, Elsevier, vol. 21(5), pages 563-580, May.
    18. K. De Brabanter & Y. Liu & C. Hua, 2016. "Convergence rates for uniform confidence intervals based on local polynomial regression estimators," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(1), pages 31-48, March.
    19. Eibelshäuser, Steffen & Wilhelm, Sascha, 2017. "Markets Take Breaks: Dynamic Price Competition with Opening Hours," VfS Annual Conference 2017 (Vienna): Alternative Structures for Money and Banking 168247, Verein für Socialpolitik / German Economic Association.
    20. Heiler, Siegfried, 1999. "A Survey on Nonparametric Time Series Analysis," CoFE Discussion Papers 99/05, University of Konstanz, Center of Finance and Econometrics (CoFE).

    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:zbw:kondp2:344. 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: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/fwkonde.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.