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Generalized F test for high dimensional linear regression coefficients

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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