IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v33y2024i4d10.1007_s11749-024-00941-x.html
   My bibliography  Save this article

Jackknife empirical likelihood for the correlation coefficient with additive distortion measurement errors

Author

Listed:
  • Da Chen

    (Georgia State University)

  • Linlin Dai

    (Southwestern University of Finance and Economics)

  • Yichuan Zhao

    (Georgia State University)

Abstract

The correlation coefficient is fundamental in advanced statistical analysis. However, traditional methods of calculating correlation coefficients can be biased due to the existence of confounding variables. Such confounding variables could act in an additive or multiplicative fashion. To study the additive model, previous research has shown residual-based estimation of correlation coefficients. The powerful tool of empirical likelihood (EL) has been used to construct the confidence interval for the correlation coefficient. However, the methods so far only perform well when sample sizes are large. With small sample size situations, the coverage probability of EL, for instance, can be below 90% at confidence level 95%. On the basis of previous research, we propose new methods of interval estimation for the correlation coefficient using jackknife empirical likelihood, mean jackknife empirical likelihood and adjusted jackknife empirical likelihood. For better performance with small sample sizes, we also propose mean adjusted empirical likelihood. The simulation results show the best performance with mean adjusted jackknife empirical likelihood when the sample sizes are as small as 25. Real data analyses are used to illustrate the proposed approach.

Suggested Citation

  • Da Chen & Linlin Dai & Yichuan Zhao, 2024. "Jackknife empirical likelihood for the correlation coefficient with additive distortion measurement errors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 33(4), pages 1129-1159, December.
    • Handle: RePEc:spr:testjl:v:33:y:2024:i:4:d:10.1007_s11749-024-00941-x
    DOI: 10.1007/s11749-024-00941-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11749-024-00941-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11749-024-00941-x?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. Ming Zheng & Wen Yu, 2013. "Empirical likelihood method for multivariate Cox regression," Computational Statistics, Springer, vol. 28(3), pages 1241-1267, June.
    3. Liang, Wei & Dai, Hongsheng & He, Shuyuan, 2019. "Mean Empirical Likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 155-169.
    4. Weichang Yu & Howard D. Bondell, 2024. "Variational Bayes for Fast and Accurate Empirical Likelihood Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 119(546), pages 1089-1101, April.
    5. 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.
    6. 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.
    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. Zhang, Jun & Feng, Zhenghui & Zhou, Bu, 2014. "A revisit to correlation analysis for distortion measurement error data," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 116-129.
    9. Y Cheng & Y Zhao, 2019. "Bayesian jackknife empirical likelihood," Biometrika, Biometrika Trust, vol. 106(4), pages 981-988.
    10. Nicole A. Lazar, 2003. "Bayesian empirical likelihood," Biometrika, Biometrika Trust, vol. 90(2), pages 319-326, June.
    11. Lei Huang & Li Zhang & Yichuan Zhao, 2024. "Jackknife empirical likelihood for the lower-mean ratio," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 36(2), pages 287-312, April.
    12. Zhenghui Feng & Jun Zhang & Qian Chen, 2020. "Statistical inference for linear regression models with additive distortion measurement errors," Statistical Papers, Springer, vol. 61(6), pages 2483-2509, December.
    13. Kangni Alemdjrodo & Yichuan Zhao, 2019. "Reduce the computation in jackknife empirical likelihood for comparing two correlated Gini indices," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 31(4), pages 849-866, October.
    14. Harrison, David Jr. & Rubinfeld, Daniel L., 1978. "Hedonic housing prices and the demand for clean air," Journal of Environmental Economics and Management, Elsevier, vol. 5(1), pages 81-102, March.
    15. Cheng, Guang & Zhao, Yichuan & Li, Bo, 2012. "Empirical likelihood inferences for the semiparametric additive isotonic regression," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 172-182.
    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. 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.
    18. Jun Zhang & Junpeng Zhu & Yan Zhou & Xia Cui & Tao Lu, 2020. "Multiplicative regression models with distortion measurement errors," Statistical Papers, Springer, vol. 61(5), pages 2031-2057, October.
    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. Yongcheng Qi, 2018. "Jackknife Empirical Likelihood Methods," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 7(2), pages 20-22, June.
    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. Khan, Ruhul Ali, 2023. "Two-sample nonparametric test for proportional reversed hazards," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    4. 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.
    5. 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.
    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. Yawen Fan & Xiaohui Liu & Yang Cao & Shaochu Liu, 2024. "Jackknife empirical likelihood based diagnostic checking for Ar(p) models," Computational Statistics, Springer, vol. 39(5), pages 2479-2509, July.
    8. Lisa Parveen & Ruhul Ali Khan & Murari Mitra, 2024. "A two sample nonparametric test for variability via empirical likelihood methods," Statistical Papers, Springer, vol. 65(7), pages 4243-4265, September.
    9. 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.
    10. Jun Zhang & Bingqing Lin & Yan Zhou, 2024. "Linear regression models with multiplicative distortions under new identifiability conditions," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 78(1), pages 25-67, February.
    11. Yinjun Chen & Hao Ming & Hu Yang, 2024. "Efficient variable selection for high-dimensional multiplicative models: a novel LPRE-based approach," Statistical Papers, Springer, vol. 65(6), pages 3713-3737, August.
    12. 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.
    13. Liang, Wei & Dai, Hongsheng & He, Shuyuan, 2019. "Mean Empirical Likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 155-169.
    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. Huilan Liu & Xiawei Zhang & Huaiqing Hu & Junjie Ma, 2024. "Analysis of the positive response data with the varying coefficient partially nonlinear multiplicative model," Statistical Papers, Springer, vol. 65(5), pages 3063-3092, July.
    16. 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.
    17. Jun Zhang, 2021. "Model checking for multiplicative linear regression models with mixed estimators," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(3), pages 364-403, August.
    18. 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.
    19. Jianhong Shi & Qian Yang & Xiongya Li & Weixing Song, 2017. "Effects of measurement error on a class of single-index varying coefficient regression models," Computational Statistics, Springer, vol. 32(3), pages 977-1001, September.
    20. Villalonga, Belen, 2004. "Intangible resources, Tobin's q, and sustainability of performance differences," Journal of Economic Behavior & Organization, Elsevier, vol. 54(2), pages 205-230, June.

    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:spr:testjl:v:33:y:2024:i:4:d:10.1007_s11749-024-00941-x. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.