IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v38y2011i11p2533-2545.html
   My bibliography  Save this article

Statistical learning theory for fitting multimodal distribution to rainfall data: an application

Author

Listed:
  • Himadri Ghosh
  • Prajneshu

Abstract

The promising methodology of the “Statistical Learning Theory” for the estimation of multimodal distribution is thoroughly studied. The “tail” is estimated through Hill's, UH and moment methods. The threshold value is determined by nonparametric bootstrap and the minimum mean square error criterion. Further, the “body” is estimated by the nonparametric structural risk minimization method of the empirical distribution function under the regression set-up. As an illustration, rainfall data for the meteorological subdivision of Orissa, India during the period 1871--2006 are used. It is shown that Hill's method has performed the best for tail density. Finally, the combined estimated “body” and “tail” of the multimodal distribution is shown to capture the multimodality present in the data.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:38:y:2011:i:11:p:2533-2545
    DOI: 10.1080/02664763.2011.559210
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/02664763.2011.559210
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664763.2011.559210?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
    ---><---

    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. Einmahl, J. H.J. & Dekkers, A. L.M. & de Haan, L., 1989. "A moment estimator for the index of an extreme-value distribution," Other publications TiSEM 81970cb3-5b7a-4cad-9bf6-2, Tilburg University, School of Economics and Management.
    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. Caers, Jef & Dyck, Jozef Van, 1998. "Nonparametric tail estimation using a double bootstrap method," Computational Statistics & Data Analysis, Elsevier, vol. 29(2), pages 191-211, December.
    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. Wager, Stefan, 2014. "Subsampling extremes: From block maxima to smooth tail estimation," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 335-353.
    2. Małgorzata Just & Krzysztof Echaust, 2021. "An Optimal Tail Selection in Risk Measurement," Risks, MDPI, vol. 9(4), pages 1-16, April.
    3. 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.
    4. 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.
    5. Christian Schluter, 2021. "On Zipf’s law and the bias of Zipf regressions," Empirical Economics, Springer, vol. 61(2), pages 529-548, August.
    6. 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.
    7. Chao Huang & Jin-Guan Lin & Yan-Yan Ren, 2012. "Statistical Inferences for Generalized Pareto Distribution Based on Interior Penalty Function Algorithm and Bootstrap Methods and Applications in Analyzing Stock Data," Computational Economics, Springer;Society for Computational Economics, vol. 39(2), pages 173-193, February.
    8. Caers, Jef & Dyck, Jozef Van, 1998. "Nonparametric tail estimation using a double bootstrap method," Computational Statistics & Data Analysis, Elsevier, vol. 29(2), pages 191-211, December.
    9. Krzysztof Echaust & Małgorzata Just, 2020. "Value at Risk Estimation Using the GARCH-EVT Approach with Optimal Tail Selection," Mathematics, MDPI, vol. 8(1), pages 1-24, January.
    10. EL-NOUTY Charles & GUILLOU Armelle, 2000. "On The Bootstrap Accuracy Of The Pareto Index," Statistics & Risk Modeling, De Gruyter, vol. 18(3), pages 275-290, March.
    11. Tsourti, Zoi & Panaretos, John, 2003. "Extreme Value Index Estimators and Smoothing Alternatives: A Critical Review," MPRA Paper 6390, University Library of Munich, Germany.
    12. 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.
    13. Geluk, J. L. & Peng, Liang, 2000. "An adaptive optimal estimate of the tail index for MA(l) time series," Statistics & Probability Letters, Elsevier, vol. 46(3), pages 217-227, February.
    14. Kim, Joseph H.T. & Kim, Joocheol, 2015. "A parametric alternative to the Hill estimator for heavy-tailed distributions," Journal of Banking & Finance, Elsevier, vol. 54(C), pages 60-71.
    15. 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.
    16. Drees, Holger & Kaufmann, Edgar, 1998. "Selecting the optimal sample fraction in univariate extreme value estimation," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 149-172, July.
    17. Hsieh, Ping-Hung, 2002. "An exploratory first step in teletraffic data modeling: evaluation of long-run performance of parameter estimators," Computational Statistics & Data Analysis, Elsevier, vol. 40(2), pages 263-283, August.
    18. Caers, Jef & Beirlant, Jan & Vynckier, Petra, 1998. "Bootstrap confidence intervals for tail indices," Computational Statistics & Data Analysis, Elsevier, vol. 26(3), pages 259-277, January.
    19. 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.
    20. Bertail, Patrice & Haefke, Christian & Politis, D.N.Dimitris N. & White, Halbert, 2004. "Subsampling the distribution of diverging statistics with applications to finance," Journal of Econometrics, Elsevier, vol. 120(2), pages 295-326, June.

    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:taf:japsta:v:38:y:2011:i:11:p:2533-2545. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    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.