Skip to main content
Log in

Jackknife empirical likelihood based inference for probability weighted moments

  • Research Article
  • Published:
Journal of the Korean Statistical Society Aims and scope Submit manuscript

Abstract

We discuss jackknife empirical likelihood (JEL) and adjusted jackknife empirical likelihood (AJEL) based inference for finding confidence intervals for probability weighted moment (PWM). We obtain the asymptotic distribution of the JEL ratio and AJEL ratio statistics. We compare the performance of the proposed confidence intervals with recently developed methods in terms of coverage probability and average width. We also develop JEL and AJEL based tests for PWM and study its properties. Finally we illustrate our method using rainfall data of Indian states.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Chen, J., Variyath, A. M., & Abraham, B. (2008). Adjusted empirical likelihood and its properties. Journal of Computational and Graphical Statistics, 17, 426–443.

    Article  MathSciNet  Google Scholar 

  • David, H. A., & Nagaraja, H. N. (2003). Order Statistics. New York: John Wiley and Sons.

    Book  Google Scholar 

  • Greenwood, J. A., Landwehr, J. M., Matalas, N. C., & Wallis, J. R. (1979). Probability weighted moments. Water Resource Research, 15, 1055–1064.

    Article  Google Scholar 

  • Hoeffding, W. (1948). A class of statistics with asymptotically normal distribution. The annals of mathematical statistics, 19, 293–325.

    Article  MathSciNet  Google Scholar 

  • Hosking, J. R. M., Wallis, J. R., & Wood, E. F. (1985). Estimation of the generalized extreme-value distribution by the method of probability-weighted moments. Technometrics, 27, 251–261.

    Article  MathSciNet  Google Scholar 

  • Jing, B. Y., Yuan, J., & Zhou, W. (2009). Jackknife empirical likelihood. Journal of the American Statistical Association, 104, 1224–1232.

    Article  MathSciNet  Google Scholar 

  • Lee, A. J. (1990). U-Statistics: Theory and Practice. New York: Marcel Dekker Inc.

    MATH  Google Scholar 

  • Lehmann, E. L. (1951). Consistency and unbiasedness of certain nonparametric tests. The Annals of Mathematical Statistics, 22, 165–179.

    Article  MathSciNet  Google Scholar 

  • Owen, A. (1990). Empirical likelihood ratio confidence regions. The Annals of Statistics, 77, 90–120.

    Article  MathSciNet  Google Scholar 

  • Owen, A. B. (1988). Empirical likelihood ratio confidence intervals for a single functional. Biometrika, 75, 237–249.

    Article  MathSciNet  Google Scholar 

  • Owen, A. B. (2001). Empirical Likelihood. New York: Chapman & Hall/CRC.

    Book  Google Scholar 

  • Peng, L. (2011). Empirical likelihood methods for the Gini index. Australian & New Zealand Journal of Statistics, 53, 131–139.

    Article  MathSciNet  Google Scholar 

  • Qin, G., Yang, B., & Hall, N. E. B. (2013). Empirical likelihood based inferences for Lorenz curve. Annals of Institute of Statistical Mathematics, 65, 1–21.

    Article  MathSciNet  Google Scholar 

  • Qin, Y., Rao, J. N. K., & Wu, C. (2010). Empirical likelihood confidence intervals for the Gini measure of income inequality. Economic Modelling, 27, 1429–1435.

    Article  Google Scholar 

  • Shi, J., & Lau, T. S. (2000). Empirical likelihood for partially linear models. Journal of Multivariate analysis, 72, 132–148.

    Article  MathSciNet  Google Scholar 

  • Shi, X. (1984). The approximate independence of jackknife pseudo-values and the bootstrap methods. Journal of Wuhan Institute Hydra-Electric Engineering, 2, 83–90.

    Google Scholar 

  • Thomas, D. R., & Grunkemeier, G. L. (1975). Confidence interval estimation of survival probabilities for censoblue data. Journal of the American Statistical Association, 70, 865–871.

    Article  MathSciNet  Google Scholar 

  • Tsao, M. (2004). Bounds on coverage probabilities of the empirical likelihood ratio confidence regions. The Annals of Statistics, 32, 1215–1221.

    Article  MathSciNet  Google Scholar 

  • Vexler, A., Zou, L., & Hutson, A. D. (2017). An extension to empirical likelihood for evaluating probability weighted moments. Journal of Statistical Planning and Inference, 182, 50–60.

    Article  MathSciNet  Google Scholar 

  • Wang, D., & Zhao, Y. (2016). Jackknife empirical likelihood for comparing two Gini indices. Canadian Journal of Statistics, 44, 102–119.

    Article  MathSciNet  Google Scholar 

  • Wang, D., Zhao, Y., & Gilmore, D. W. (2016). Jackknife empirical likelihood confidence interval for the Gini index. Statistics & Probability Letters, 110, 289–295.

    Article  MathSciNet  Google Scholar 

  • Vexler, A., & Yu, J. (2018). Empirical Likelihood Methods in Biomedicine and Health. CRC Press, Boca Raton: Chapman and Hall.

    Book  Google Scholar 

  • Whang, Y. J. (2006). Smoothed empirical likelihood methods for quantile regression models. Econometric Theory, 22, 173–205.

    Article  MathSciNet  Google Scholar 

  • Zhao, Y., Meng, X., & Yang, H. (2015). Jackknife empirical likelihood inference for the mean absolute deviation. Computational Statistics & Data Analysis, 91, 92–101.

    Article  MathSciNet  Google Scholar 

  • Zhou, M. (2015). Empirical likelihood method in survival analysis. Boca Raton: Chapman and Hall, CRC Press.

    Book  Google Scholar 

Download references

Acknowledgements

We thank the anonymous referees for their constructive suggestions that help to improve the presentation of the paper substantially. Deepesh Bhati would like to thanks Indian Statistical Institute, Chennai for the support during his visit to ISI Chennai.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sudheesh K. Kattumannil.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bhati, D., Kattumannil, S.K. & Sreelakshmi, N. Jackknife empirical likelihood based inference for probability weighted moments. J. Korean Stat. Soc. 50, 98–116 (2021). https://doi.org/10.1007/s42952-020-00062-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42952-020-00062-9

Keywords

Navigation