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A generalized likelihood ratio test for normal mean when p is greater than n

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  • Zhao, Junguang
  • Xu, Xingzhong

Abstract

The problem of testing the population mean vector of high-dimensional multivariate data is considered. Inspired by Roy’s union–intersection test, a generalized high-dimensional likelihood ratio test for the normal population mean vector is proposed. The p-value for the test is obtained by using randomization method, which does not rely on assumptions about the structure of the covariance matrix. An interpretation of the new statistic is given, which does not rely on the normality assumption. Hence the proposed test is also available for non-normal multivariate population. Simulation studies show that the new test offers higher power than other two competing tests when the variables are dependent and performs particularly well for non-normal multivariate population.

Suggested Citation

  • Zhao, Junguang & Xu, Xingzhong, 2016. "A generalized likelihood ratio test for normal mean when p is greater than n," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 91-104.
    • Handle: RePEc:eee:csdana:v:99:y:2016:i:c:p:91-104
    DOI: 10.1016/j.csda.2016.01.006
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    Cited by:

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    3. Ouyang, Yanyan & Liu, Jiamin & Tong, Tiejun & Xu, Wangli, 2022. "A rank-based high-dimensional test for equality of mean vectors," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    4. Zhang, Qiuyan & Wang, Chen & Zhang, Baoxue & Yang, Hu, 2024. "An RIHT statistic for testing the equality of several high-dimensional mean vectors under homoskedasticity," Computational Statistics & Data Analysis, Elsevier, vol. 190(C).
    5. Zongliang Hu & Tiejun Tong & Marc G. Genton, 2019. "Diagonal likelihood ratio test for equality of mean vectors in high‐dimensional data," Biometrics, The International Biometric Society, vol. 75(1), pages 256-267, March.
    6. Zhao, Li & Xu, Xingzhong, 2017. "Generalized canonical correlation variables improved estimation in high dimensional seemingly unrelated regression models," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 119-126.

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