IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v54y2010i2p509-515.html
   My bibliography  Save this article

On nonparametric local inference for density estimation

Author

Listed:
  • Chan, Ngai-Hang
  • Lee, Thomas C.M.
  • Peng, Liang

Abstract

Bandwidth selection has been an important topic in nonparametric density estimation. In this paper an effective method for local bandwidth selection is proposed. For local bandwidth selection, due to data sparsity and other reasons, extremely small bandwidths are sometimes selected, which lead to severe undersmoothing. To circumvent this difficulty, the main idea behind the proposed method is to choose the largest bandwidth that still achieves the optimal rate. When coupled with practical bias reduction techniques, the bandwidth selected from this method can be applied simultaneously to conduct both local point and interval estimation. Simulation studies demonstrate the effectiveness of the proposed approach, which compares favorably with other existing approaches.

Suggested Citation

  • Chan, Ngai-Hang & Lee, Thomas C.M. & Peng, Liang, 2010. "On nonparametric local inference for density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 509-515, February.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:2:p:509-515
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(09)00351-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. Armelle Guillou & Peter Hall, 2001. "A diagnostic for selecting the threshold in extreme value analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 293-305.
    2. Sheather, Simon, 1983. "A data-based algorithm for choosing the window width when estimating the density at a point," Computational Statistics & Data Analysis, Elsevier, vol. 1(1), pages 229-238, March.
    3. Hall, Peter, 1990. "Using the bootstrap to estimate mean squared error and select smoothing parameter in nonparametric problems," Journal of Multivariate Analysis, Elsevier, vol. 32(2), pages 177-203, February.
    4. Einmahl, John H. J., 1997. "Poisson and Gaussian approximation of weighted local empirical processes," Stochastic Processes and their Applications, Elsevier, vol. 70(1), pages 31-58, October.
    5. Sheather, Simon J., 1986. "An improved data-based algorithm for choosing the window width when estimating the density at a point," Computational Statistics & Data Analysis, Elsevier, vol. 4(1), pages 61-65, June.
    6. Peter Hall & Michael C. Minnotte, 2002. "High order data sharpening for density estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(1), pages 141-157, January.
    7. Ziegler Klaus, 2006. "On local bootstrap bandwidth choice in kernel density estimation," Statistics & Risk Modeling, De Gruyter, vol. 24(2), pages 291-301, December.
    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. 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.
    2. Golyandina, Nina & Pepelyshev, Andrey & Steland, Ansgar, 2012. "New approaches to nonparametric density estimation and selection of smoothing parameters," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2206-2218.

    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. 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.
    2. Wager, Stefan, 2014. "Subsampling extremes: From block maxima to smooth tail estimation," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 335-353.
    3. Małgorzata Just & Krzysztof Echaust, 2021. "An Optimal Tail Selection in Risk Measurement," Risks, MDPI, vol. 9(4), pages 1-16, April.
    4. M. Ivette Gomes & Armelle Guillou, 2015. "Extreme Value Theory and Statistics of Univariate Extremes: A Review," International Statistical Review, International Statistical Institute, vol. 83(2), pages 263-292, August.
    5. Juan Gonzalez & Daniela Rodriguez & Mariela Sued, 2013. "Threshold selection for extremes under a semiparametric model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 22(4), pages 481-500, November.
    6. Farmen, Mark & Marron, J. S., 1999. "An assessment of finite sample performance of adaptive methods in density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 30(2), pages 143-168, April.
    7. Wang, Yinzhi & Hobæk Haff, Ingrid & Huseby, Arne, 2020. "Modelling extreme claims via composite models and threshold selection methods," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 257-268.
    8. Himadri Ghosh & Prajneshu, 2011. "Statistical learning theory for fitting multimodal distribution to rainfall data: an application," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(11), pages 2533-2545, January.
    9. Oliveira, M. & Crujeiras, R.M. & Rodríguez-Casal, A., 2012. "A plug-in rule for bandwidth selection in circular density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3898-3908.
    10. Luc Devroye & Gábor Lugosi, 1998. "Variable Kernel estimates: On the impossibility of tuning the parameters," Economics Working Papers 325, Department of Economics and Business, Universitat Pompeu Fabra.
    11. Danielsson, J. & de Haan, L. & Peng, L. & de Vries, C. G., 2001. "Using a Bootstrap Method to Choose the Sample Fraction in Tail Index Estimation," Journal of Multivariate Analysis, Elsevier, vol. 76(2), pages 226-248, February.
    12. Barunik, Jozef & Vacha, Lukas, 2010. "Monte Carlo-based tail exponent estimator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4863-4874.
    13. Einmahl, John & Yang, Fan & Zhou, Chen, 2018. "Testing the Multivariate Regular Variation Model," Other publications TiSEM dd3c4dd0-7181-40f3-af44-f, Tilburg University, School of Economics and Management.
    14. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    15. Chen, Zhimin & Ibragimov, Rustam, 2019. "One country, two systems? The heavy-tailedness of Chinese A- and H- share markets," Emerging Markets Review, Elsevier, vol. 38(C), pages 115-141.
    16. Claudia Klüppelberg & Gabriel Kuhn & Liang Peng, 2008. "Semi‐Parametric Models for the Multivariate Tail Dependence Function – the Asymptotically Dependent Case," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(4), pages 701-718, December.
    17. Wang, Yulong & Xiao, Zhijie, 2022. "Estimation and inference about tail features with tail censored data," Journal of Econometrics, Elsevier, vol. 230(2), pages 363-387.
    18. Einmahl, J.H.J. & de Haan, L.F.M. & Piterbarg, V.I., 2001. "Nonparametric estimation of the spectral measure of an extreme value distribution," Other publications TiSEM c3485b9b-a0bd-456f-9baa-0, Tilburg University, School of Economics and Management.
    19. Dominique Guegan & Bertrand K. Hassani, 2011. "Operational risk: a Basel II++ step before Basel III," Documents de travail du Centre d'Economie de la Sorbonne 11053, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    20. Einmahl, J.H.J. & Krajina, A. & Segers, J., 2011. "An M-Estimator for Tail Dependence in Arbitrary Dimensions," Discussion Paper 2011-013, Tilburg University, Center for Economic Research.

    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:eee:csdana:v:54:y:2010:i:2:p:509-515. 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/locate/csda .

    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.