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Semi-parametric Estimation for Selecting Optimal Threshold of Extreme Rainfall Events

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  • Wendy Shinyie
  • Noriszura Ismail
  • Abdul Jemain

Abstract

The two primary approaches of extreme events analysis are annual maximum series (AMS), which fits Generalized Extreme Value (GEV) distribution to the yearly peaks of events in the observation period, and partial duration series (PDS), which fits Generalized Pareto (GP) distribution to the peaks of events that exceed a given threshold. The PDS is able to reduce sampling uncertainty and is more useful in dealing with extreme values and asymmetries in the tails, but the optimal threshold is required. The objective of this study is to compare and determine the best method for selecting the optimal threshold of PDS using the hourly, 12-h and 24-h aggregated data of rainfall time series in Peninsular Malaysia. The choice of the threshold, or the number of largest order statistics, can be estimated by the parameters of extreme events. In this study, thirteen semi-parametric estimators are considered and applied to estimate the shape parameter or extreme value index (EVI). A semi-parametric bootstrap is then used to estimate the mean square error (MSE) of the estimator at each threshold and the optimal threshold is selected based on the smallest MSE. Based on the smallest MSE, the majority of stations and data durations favor the Adapted Hill estimator, followed by the QQ, Hill and Moment Ratio 1 estimators. Therefore, this study proves that the application of different estimators on real data may result in different optimal values of threshold and the choice of the best method is very much data-dependent. Copyright Springer Science+Business Media Dordrecht 2013

Suggested Citation

  • Wendy Shinyie & Noriszura Ismail & Abdul Jemain, 2013. "Semi-parametric Estimation for Selecting Optimal Threshold of Extreme Rainfall Events," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 27(7), pages 2325-2352, May.
    • Handle: RePEc:spr:waterr:v:27:y:2013:i:7:p:2325-2352
    DOI: 10.1007/s11269-013-0290-7
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    References listed on IDEAS

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    1. Russell Davidson, 2012. "Statistical inference in the presence of heavy tails," Econometrics Journal, Royal Economic Society, vol. 15(1), pages 31-53, February.
    2. Lingling Zhao & Jun Xia & Leszek Sobkowiak & Zhonggen Wang & Fengrui Guo, 2012. "Spatial Pattern Characterization and Multivariate Hydrological Frequency Analysis of Extreme Precipitation in the Pearl River Basin, China," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(12), pages 3619-3637, September.
    3. Jesus Gonzalo, 2004. "Which Extreme Values Are Really Extreme?," Journal of Financial Econometrics, Oxford University Press, vol. 2(3), pages 349-369.
    4. Amir AghaKouchak & Nasrin Nasrollahi, 2010. "Semi-parametric and Parametric Inference of Extreme Value Models for Rainfall Data," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 24(6), pages 1229-1249, April.
    5. Zahrahtul Zakaria & Ani Shabri & Ummi Ahmad, 2012. "Regional Frequency Analysis of Extreme Rainfalls in the West Coast of Peninsular Malaysia using Partial L-Moments," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 26(15), pages 4417-4433, December.
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    Cited by:

    1. L. Vasiliades & P. Galiatsatou & A. Loukas, 2015. "Nonstationary Frequency Analysis of Annual Maximum Rainfall Using Climate Covariates," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 29(2), pages 339-358, January.
    2. Wendy Shinyie & Noriszura Ismail & Abdul Jemain, 2014. "Semi-parametric Estimation Based on Second Order Parameter for Selecting Optimal Threshold of Extreme Rainfall Events," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(11), pages 3489-3514, September.

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