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Smoothed jackknife empirical likelihood method for ROC curve

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  • Gong, Yun
  • Peng, Liang
  • Qi, Yongcheng

Abstract

In this paper we propose a smoothed jackknife empirical likelihood method to construct confidence intervals for the receiver operating characteristic (ROC) curve. By applying the standard empirical likelihood method for a mean to the jackknife sample, the empirical likelihood ratio statistic can be calculated by simply solving a single equation. Therefore, this procedure is easy to implement. Wilks' theorem for the empirical likelihood ratio statistic is proved and a simulation study is conducted to compare the performance of the proposed method with other methods.

Suggested Citation

  • Gong, Yun & Peng, Liang & Qi, Yongcheng, 2010. "Smoothed jackknife empirical likelihood method for ROC curve," Journal of Multivariate Analysis, Elsevier, vol. 101(6), pages 1520-1531, July.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:6:p:1520-1531
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    2. Harold D Chiang & Yukitoshi Matsushita & Taisuke Otsu, 2021. "Multiway empirical likelihood," Papers 2108.04852, arXiv.org, revised Dec 2023.
    3. Yang, Hanfang & Zhao, Yichuan, 2013. "Smoothed jackknife empirical likelihood inference for the difference of ROC curves," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 270-284.
    4. Zhouping Li & Jinfeng Xu & Wang Zhou, 2016. "On Nonsmooth Estimating Functions via Jackknife Empirical Likelihood," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 49-69, March.
    5. Harold D Chiang & Yukitoshi Matsushita & Taisuke Otsu, 2021. "Multiway empirical likelihood," STICERD - Econometrics Paper Series 617, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    6. Liu, Aiai & Hou, Yanxi & Peng, Liang, 2015. "Interval estimation for a measure of tail dependence," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 294-305.
    7. Yueheng An & Yichuan Zhao, 2018. "Jackknife empirical likelihood for the difference of two volumes under ROC surfaces," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(4), pages 789-806, August.
    8. Hanfang Yang & Yichuan Zhao, 2017. "Smoothed jackknife empirical likelihood for the difference of two quantiles," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(5), pages 1059-1073, October.
    9. Zhao, Yichuan & Su, Yueju & Yang, Hanfang, 2020. "Jackknife empirical likelihood inference for the Pietra ratio," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    10. Ai-Ai Liu & Han-Ying Liang, 2017. "Jackknife empirical likelihood of error variance in partially linear varying-coefficient errors-in-variables models," Statistical Papers, Springer, vol. 58(1), pages 95-122, March.
    11. Hui-Ling Lin & Zhouping Li & Dongliang Wang & Yichuan Zhao, 2017. "Jackknife empirical likelihood for the error variance in linear models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(2), pages 151-166, April.
    12. Yukitoshi Matsushita & Taisuke Otsu, 2019. "Jackknife, small bandwidth and high-dimensional asymptotics," STICERD - Econometrics Paper Series 605, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    13. Zhang, Xiuzhen & Lu, Zhiping & Wang, Yangye & Zhang, Riquan, 2020. "Adjusted jackknife empirical likelihood for stationary ARMA and ARFIMA models," Statistics & Probability Letters, Elsevier, vol. 165(C).
    14. Zhang, Zhigang & Zhao, Yichuan, 2013. "Empirical likelihood for linear transformation models with interval-censored failure time data," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 398-409.
    15. Harold D. Chiang & Bing Yang Tan, 2020. "Empirical likelihood and uniform convergence rates for dyadic kernel density estimation," Papers 2010.08838, arXiv.org, revised May 2022.
    16. Yang, Hanfang & Zhao, Yichuan, 2015. "Smoothed jackknife empirical likelihood inference for ROC curves with missing data," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 123-138.
    17. Shan Luo & Gengsheng Qin, 2017. "New non-parametric inferences for low-income proportions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(3), pages 599-626, June.
    18. Zang, Yangguang & Zhang, Sanguo & Li, Qizhai & Zhang, Qingzhao, 2016. "Jackknife empirical likelihood test for high-dimensional regression coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 302-316.
    19. Feng, Huijun & Peng, Liang, 2012. "Jackknife empirical likelihood tests for error distributions in regression models," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 63-75.
    20. Yang, Hanfang & Zhao, Yichuan, 2018. "Smoothed jackknife empirical likelihood for the one-sample difference of quantiles," Computational Statistics & Data Analysis, Elsevier, vol. 120(C), pages 58-69.
    21. Zhao, Yichuan & Meng, Xueping & Yang, Hanfang, 2015. "Jackknife empirical likelihood inference for the mean absolute deviation," Computational Statistics & Data Analysis, Elsevier, vol. 91(C), pages 92-101.
    22. Yongcheng Qi, 2018. "Jackknife Empirical Likelihood Methods," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 7(2), pages 20-22, June.

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