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Tests for high dimensional generalized linear models

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  • Bin Guo
  • Song Xi Chen

Abstract

We consider testing regression coefficients in high dimensional generalized linear models. By modifying a test statistic proposed by Goeman et al. (2011) for large but fixed dimensional settings, we propose a new test which is applicable for diverging dimension and is robust for a wide range of link functions. The power properties of the tests are evaluated under the setting of the local and fixed alternatives. A test in the presence of nuisance parameters is also proposed. The proposed tests can provide p-values for testing significance of multiple gene-sets, whose usefulness is demonstrated in a case study on an acute lymphoblastic leukemia dataset.
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Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssb:v:78:y:2016:i:5:p:1079-1102
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    1. 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.
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    4. 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.
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    11. 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.
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    Cited by:

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    2. Sardy, Sylvain & Diaz-Rodriguez, Jairo & Giacobino, Caroline, 2022. "Thresholding tests based on affine LASSO to achieve non-asymptotic nominal level and high power under sparse and dense alternatives in high dimension," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    3. Feng, Long & Zhang, Xiaoxu & Liu, Binghui, 2020. "Multivariate tests of independence and their application in correlation analysis between financial markets," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    4. Simona Catuogno & Claudia Arena & Sara Saggese & Fabrizia Sarto, 2016. "The Influence of Blockholders, Bondholders and Families on the Venturers’ Accounting Behavior," International Journal of Business and Management, Canadian Center of Science and Education, vol. 11(8), pages 1-31, July.
    5. Liu, Yang & Sun, Wei & Hsu, Li & He, Qianchuan, 2022. "Statistical inference for high-dimensional pathway analysis with multiple responses," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    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. Yi He & Sombut Jaidee & Jiti Gao, 2020. "Most Powerful Test against High Dimensional Free Alternatives," Monash Econometrics and Business Statistics Working Papers 13/20, Monash University, Department of Econometrics and Business Statistics.
    8. Zhou, Ping & Yu, Zhen & Ma, Jingyi & Tian, Maozai & Fan, Ye, 2021. "Communication-efficient distributed estimator for generalized linear models with a diverging number of covariates," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).

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    More about this item

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

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