IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v117y2013icp134-149.html
   My bibliography  Save this article

Generalized F test for high dimensional linear regression coefficients

Author

Listed:
  • Wang, Siyang
  • Cui, Hengjian

Abstract

To test the regression coefficients of linear models, the conventional F-test has been suggested. This paper investigates the performance of the generalized F-test for testing regression coefficients in high dimensional linear regression under the case of p/n⟶ρ(0<ρ<1). The asymptotic normality of generalized F-statistic is obtained under some regular conditions, and then the power of the F-test is derived. Some comparisons and an illustrated example are also presented.

Suggested Citation

  • Wang, Siyang & Cui, Hengjian, 2013. "Generalized F test for high dimensional linear regression coefficients," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 134-149.
    • Handle: RePEc:eee:jmvana:v:117:y:2013:i:c:p:134-149
    DOI: 10.1016/j.jmva.2013.02.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X13000249
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2013.02.010?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. 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.
    2. Bhansali, R.J. & Giraitis, L. & Kokoszka, P.S., 2007. "Convergence of quadratic forms with nonvanishing diagonal," Statistics & Probability Letters, Elsevier, vol. 77(7), pages 726-734, April.
    3. Fan, Jianqing & Hall, Peter & Yao, Qiwei, 2007. "To How Many Simultaneous Hypothesis Tests Can Normal, Student's t or Bootstrap Calibration Be Applied?," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1282-1288, December.
    4. 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.
    5. 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.
    6. Huang, Jian & Wang, Deli & Zhang, Cun-Hui, 2005. "A Two-Way Semilinear Model for Normalization and Analysis of cDNA Microarray Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 814-829, September.
    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. 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.
    2. Ping-Shou Zhong & Tao Hu & Jun Li, 2015. "Tests for Coefficients in High-dimensional Additive Hazard Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 649-664, September.
    3. Jiang Dandan & Sun Jianguo, 2017. "Group Tests for High-dimensional Failure Time Data with the Additive Hazards Models," The International Journal of Biostatistics, De Gruyter, vol. 13(1), pages 1-10, May.
    4. Ueki, Masao, 2021. "Testing conditional mean through regression model sequence using Yanai’s generalized coefficient of determination," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).
    5. Kwon, Sanguk & Cho, Seong-Hoon & Roberts, Roland K. & Kim, Hyun Jae & Park, KiHyun & Edward Yu, Tun-Hsiang, 2016. "Short-run and the long-run effects of electricity price on electricity intensity across regions," Applied Energy, Elsevier, vol. 172(C), pages 372-382.
    6. He, Yi & Jaidee, Sombut & Gao, Jiti, 2023. "Most powerful test against a sequence of high dimensional local alternatives," Journal of Econometrics, Elsevier, vol. 234(1), pages 151-177.
    7. Audrino, Francesco & Sigrist, Fabio & Ballinari, Daniele, 2020. "The impact of sentiment and attention measures on stock market volatility," International Journal of Forecasting, Elsevier, vol. 36(2), pages 334-357.

    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. 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.
    2. Chen, Songxi, 2012. "Two Sample Tests for High Dimensional Covariance Matrices," MPRA Paper 46026, University Library of Munich, Germany.
    3. Qiang Sun & Hongtu Zhu & Yufeng Liu & Joseph G. Ibrahim, 2015. "SPReM: Sparse Projection Regression Model For High-Dimensional Linear Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 289-302, March.
    4. Qiu, Tao & Zhang, Qintong & Fang, Yuanyuan & Xu, Wangli, 2024. "Testing homogeneity in high dimensional data through random projections," Journal of Multivariate Analysis, Elsevier, vol. 200(C).
    5. Gong, Siliang & Zhang, Kai & Liu, Yufeng, 2018. "Efficient test-based variable selection for high-dimensional linear models," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 17-31.
    6. Xu, Kai & Tian, Yan & He, Daojiang, 2021. "A high dimensional nonparametric test for proportional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    7. 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.
    8. Wei Lan & Hansheng Wang & Chih-Ling Tsai, 2014. "Testing covariates in high-dimensional regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(2), pages 279-301, April.
    9. Wenjuan Hu & Nan Lin & Baoxue Zhang, 2020. "Nonparametric testing of lack of dependence in functional linear models," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-24, June.
    10. Yata, Kazuyoshi & Aoshima, Makoto, 2013. "Correlation tests for high-dimensional data using extended cross-data-matrix methodology," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 313-331.
    11. Qi Zhang, 2022. "High-Dimensional Mediation Analysis with Applications to Causal Gene Identification," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 14(3), pages 432-451, December.
    12. Ma, Yingying & Lan, Wei & Wang, Hansheng, 2015. "A high dimensional two-sample test under a low dimensional factor structure," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 162-170.
    13. Peng, Liuhua & Chen, Song Xi & Zhou, Wen, 2016. "More powerful tests for sparse high-dimensional covariances matrices," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 124-143.
    14. 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.
    15. 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.
    16. 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.
    17. Yata, Kazuyoshi & Aoshima, Makoto, 2016. "High-dimensional inference on covariance structures via the extended cross-data-matrix methodology," Journal of Multivariate Analysis, Elsevier, vol. 151(C), pages 151-166.
    18. Yue, Mu & Li, Jialiang & Cheng, Ming-Yen, 2019. "Two-step sparse boosting for high-dimensional longitudinal data with varying coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 222-234.
    19. Huang, Yuan & Li, Changcheng & Li, Runze & Yang, Songshan, 2022. "An overview of tests on high-dimensional means," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    20. Xu, Kai & Hao, Xinxin, 2019. "A nonparametric test for block-diagonal covariance structure in high dimension and small samples," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 551-567.

    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:117:y:2013:i:c:p:134-149. 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.