IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v94y2016icp302-316.html
   My bibliography  Save this article

Jackknife empirical likelihood test for high-dimensional regression coefficients

Author

Listed:
  • Zang, Yangguang
  • Zhang, Sanguo
  • Li, Qizhai
  • Zhang, Qingzhao

Abstract

A novel way to test coefficients in high-dimensional linear regression model is presented. Under the ‘large p small n’ situation, the traditional methods, like F-test and t-test, are unsuitable or undefined. The proposed jackknife empirical likelihood test has an asymptotic chi-square distribution and the conditions are much weaker than those in the existing methods. Moreover, an extension of the proposed method can test part of the regression coefficients, which is practical in considering the significance for a subset of covariates. Simulations show that the proposed test has a good control of the type-I error, and is more powerful than Zhong and Chen (2011)’s method in most cases. The proposed test is employed to analyze a rheumatoid arthritis data to find the association between rheumatoid arthritis and the SNPs on the chromosomes 6.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:94:y:2016:i:c:p:302-316
    DOI: 10.1016/j.csda.2015.08.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947315002005
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2015.08.012?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. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Jelle J. Goeman & Sara A. Van De Geer & Hans C. Van Houwelingen, 2006. "Testing against a high dimensional alternative," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(3), pages 477-493, June.
    3. Zhong, Ping-Shou & Chen, Song Xi, 2011. "Tests for High-Dimensional Regression Coefficients With Factorial Designs," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 260-274.
    4. 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.
    5. 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.
    6. Francesco Bravo, 2003. "Second-order power comparisons for a class of nonparametric likelihood-based tests," Biometrika, Biometrika Trust, vol. 90(4), pages 881-890, December.
    7. Chen, Song Xi & Zhang, Li-Xin & Zhong, Ping-Shou, 2010. "Tests for High-Dimensional Covariance Matrices," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 810-819.
    8. 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.
    9. Song Chen & Ingrid Van Keilegom, 2009. "A review on empirical likelihood methods for regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(3), pages 415-447, November.
    10. Peng, Liang & Qi, Yongcheng & Wang, Ruodu & Yang, Jingping, 2012. "Jackknife empirical likelihood method for some risk measures and related quantities," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 142-150.
    11. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
    12. Jelle J. Goeman & Hans C. van Houwelingen & Livio Finos, 2011. "Testing against a high-dimensional alternative in the generalized linear model: asymptotic type I error control," Biometrika, Biometrika Trust, vol. 98(2), pages 381-390.
    13. Chen, Song Xi & Qin, Yingli, 2010. "A Two Sample Test for High Dimensional Data with Applications to Gene-set Testing," MPRA Paper 59642, University Library of Munich, Germany.
    14. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    15. Peng, Liang & Qi, Yongcheng & Wang, Ruodu, 2014. "Empirical likelihood test for high dimensional linear models," Statistics & Probability Letters, Elsevier, vol. 86(C), pages 85-90.
    16. Song Xi Chen & Liang Peng & Ying-Li Qin, 2009. "Effects of data dimension on empirical likelihood," Biometrika, Biometrika Trust, vol. 96(3), pages 711-722.
    17. Song Chen & Ingrid Van Keilegom, 2009. "Rejoinder on: A review on empirical likelihood methods for regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(3), pages 468-474, November.
    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. Liu, Yan & Zhang, Sanguo & Ma, Shuangge & Zhang, Qingzhao, 2020. "Tests for regression coefficients in high dimensional partially linear models," Statistics & Probability Letters, Elsevier, vol. 163(C).

    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. Bin Guo & Song Xi Chen, 2016. "Tests for high dimensional generalized linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(5), pages 1079-1102, November.
    2. Qinqin Hu & Lu Lin, 2017. "Conditional sure independence screening by conditional marginal empirical likelihood," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 63-96, February.
    3. Zhao, Yichuan & Su, Yueju & Yang, Hanfang, 2020. "Jackknife empirical likelihood inference for the Pietra ratio," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    4. Hong Guo & Changliang Zou & Zhaojun Wang & Bin Chen, 2014. "Empirical likelihood for high-dimensional linear regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(7), pages 921-945, October.
    5. 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.
    6. Wang, Siyang & Cui, Hengjian, 2015. "A new test for part of high dimensional regression coefficients," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 187-203.
    7. Chang, Jinyuan & Chen, Song Xi & Chen, Xiaohong, 2015. "High dimensional generalized empirical likelihood for moment restrictions with dependent data," Journal of Econometrics, Elsevier, vol. 185(1), pages 283-304.
    8. Zhang, Jia & Shi, Haoming & Tian, Lemeng & Xiao, Fengjun, 2019. "Penalized generalized empirical likelihood in high-dimensional weakly dependent data," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 270-283.
    9. Tong Tong Wu & Gang Li & Chengyong Tang, 2015. "Empirical Likelihood for Censored Linear Regression and Variable Selection," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 798-812, September.
    10. Rui Wang & Xingzhong Xu, 2021. "A Bayesian-motivated test for high-dimensional linear regression models with fixed design matrix," Statistical Papers, Springer, vol. 62(4), pages 1821-1852, August.
    11. Ma, Yingying & Lan, Wei & Wang, Hansheng, 2015. "Testing predictor significance with ultra high dimensional multivariate responses," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 275-286.
    12. Yongcheng Qi, 2018. "Jackknife Empirical Likelihood Methods," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 7(2), pages 20-22, June.
    13. Lan, Wei & Zhong, Ping-Shou & Li, Runze & Wang, Hansheng & Tsai, Chih-Ling, 2016. "Testing a single regression coefficient in high dimensional linear models," Journal of Econometrics, Elsevier, vol. 195(1), pages 154-168.
    14. Long Feng & Changliang Zou & Zhaojun Wang, 2016. "Multivariate-Sign-Based High-Dimensional Tests for the Two-Sample Location Problem," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 721-735, April.
    15. 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.
    16. Otsu, Taisuke & Xu, Ke-Li & Matsushita, Yukitoshi, 2015. "Empirical likelihood for regression discontinuity design," Journal of Econometrics, Elsevier, vol. 186(1), pages 94-112.
    17. Shan Luo & Zehua Chen, 2014. "Sequential Lasso Cum EBIC for Feature Selection With Ultra-High Dimensional Feature Space," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1229-1240, September.
    18. Shi Chen & Wolfgang Karl Hardle & Brenda L'opez Cabrera, 2020. "Regularization Approach for Network Modeling of German Power Derivative Market," Papers 2009.09739, arXiv.org.
    19. Wang, Christina Dan & Chen, Zhao & Lian, Yimin & Chen, Min, 2022. "Asset selection based on high frequency Sharpe ratio," Journal of Econometrics, Elsevier, vol. 227(1), pages 168-188.
    20. Peter Bühlmann & Jacopo Mandozzi, 2014. "High-dimensional variable screening and bias in subsequent inference, with an empirical comparison," Computational Statistics, Springer, vol. 29(3), pages 407-430, 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:eee:csdana:v:94:y:2016:i:c:p:302-316. 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/locate/csda .

    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.