IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v140y2015icp123-138.html
   My bibliography  Save this article

Smoothed jackknife empirical likelihood inference for ROC curves with missing data

Author

Listed:
  • Yang, Hanfang
  • Zhao, Yichuan

Abstract

In this paper, we apply smoothed jackknife empirical likelihood (JEL) method to construct confidence intervals for the receiver operating characteristic (ROC) curve with missing data. After using hot deck imputation, we generate pseudo-jackknife sample to develop jackknife empirical likelihood. Comparing to traditional empirical likelihood method, the smoothed JEL has a great advantage in saving computational cost. Under mild conditions, the smoothed jackknife empirical likelihood ratio converges to a scaled chi-square distribution. Furthermore, simulation studies in terms of coverage probability and average length of confidence intervals demonstrate this proposed method has the good performance in small sample sizes. A real data set is used to illustrate our proposed JEL method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:140:y:2015:i:c:p:123-138
    DOI: 10.1016/j.jmva.2015.05.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X15001177
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2015.05.002?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. Jing, Bing-Yi & Yuan, Junqing & Zhou, Wang, 2009. "Jackknife Empirical Likelihood," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1224-1232.
    2. 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.
    3. Liang Peng & Yongcheng Qi, 2010. "Smoothed jackknife empirical likelihood method for tail copulas," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(3), pages 514-536, November.
    4. Qihua Wang & J. N. K. Rao, 2002. "Empirical Likelihood‐based Inference in Linear Models with Missing Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(3), pages 563-576, September.
    5. Lloyd, Chris J. & Yong, Zhou, 1999. "Kernel estimators of the ROC curve are better than empirical," Statistics & Probability Letters, Elsevier, vol. 44(3), pages 221-228, September.
    6. Qihua Wang, 2002. "Empirical likelihood-based inference in linear errors-in-covariables models with validation data," Biometrika, Biometrika Trust, vol. 89(2), pages 345-358, June.
    7. Anna N. Angelos Tosteson & Colin B. Begg, 1988. "A General Regression Methodology for ROC Curve Estimation," Medical Decision Making, , vol. 8(3), pages 204-215, August.
    8. 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.
    9. Chen, Jian & Peng, Liang & Zhao, Yichuan, 2009. "Empirical likelihood based confidence intervals for copulas," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 137-151, January.
    10. Rebecca R. Andridge & Roderick J. A. Little, 2010. "A Review of Hot Deck Imputation for Survey Non‐response," International Statistical Review, International Statistical Institute, vol. 78(1), pages 40-64, April.
    11. Mojirsheibani, Majid, 2001. "The Glivenko-Cantelli theorem based on data with randomly imputed missing values," Statistics & Probability Letters, Elsevier, vol. 55(4), pages 385-396, 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. 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.
    2. Ana M. Bianco & Graciela Boente & Wenceslao González–Manteiga & Ana Pérez–González, 2023. "Estimators for ROC curves with missing biomarkers values and informative covariates," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(3), pages 931-956, September.
    3. Amorim, G. & Thas, O. & Vermeulen, K. & Vansteelandt, S. & De Neve, J., 2018. "Small sample inference for probabilistic index models," Computational Statistics & Data Analysis, Elsevier, vol. 121(C), pages 137-148.
    4. 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.
    5. Zhao, Yichuan & Su, Yueju & Yang, Hanfang, 2020. "Jackknife empirical likelihood inference for the Pietra ratio," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    6. Yu, Xue & Zhao, Yichuan, 2019. "Empirical likelihood inference for semi-parametric transformation models with length-biased sampling," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 115-125.
    7. 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.
    8. Xue Yu & Yichuan Zhao, 2019. "Jackknife empirical likelihood inference for the accelerated failure time model," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 269-288, March.
    9. Yongcheng Qi, 2018. "Jackknife Empirical Likelihood Methods," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 7(2), pages 20-22, June.

    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. 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.
    2. Zhao, Yichuan & Su, Yueju & Yang, Hanfang, 2020. "Jackknife empirical likelihood inference for the Pietra ratio," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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).
    8. 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.
    9. 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.
    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. 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.
    12. 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.
    13. Yongcheng Qi, 2018. "Jackknife Empirical Likelihood Methods," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 7(2), pages 20-22, June.
    14. 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.
    15. 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.
    16. Yang Wei & Zhouping Li & Yunqiu Dai, 2022. "Unified smoothed jackknife empirical likelihood tests for comparing income inequality indices," Statistical Papers, Springer, vol. 63(5), pages 1415-1475, October.
    17. Yichuan Zhao & Ali Jinnah, 2012. "Inference for Cox’s regression models via adjusted empirical likelihood," Computational Statistics, Springer, vol. 27(1), pages 1-12, March.
    18. 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.
    19. 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.
    20. Xiaohui Liu & Qihua Wang & Yi Liu, 2017. "A consistent jackknife empirical likelihood test for distribution functions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(2), pages 249-269, April.

    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:jmvana:v:140:y:2015:i:c:p:123-138. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.