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A simple test for zero multiple correlation coefficient in high-dimensional normal data using random projection

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  • Najarzadeh, Dariush

Abstract

The multiple correlation coefficient (MCC) is a measure of linear relationship between a given variable and a set of covariates. Testing the hypothesis of zero MCC has always been important in multiple correlation analysis. For testing this hypothesis, due to the singularity of the sample covariance matrix in high-dimensional data, the classical testing procedures are no longer usable. To test the null hypothesis of zero MCC in high-dimensional normal data, a simple testing procedure is proposed by using the random projection and union-intersection methodologies. Some simulations are carried out to verify the performance evaluation of the proposed test. The results are found to be very convincing. In the end, the experimental validation of the proposed test is carried out on mice tumor data.

Suggested Citation

  • Najarzadeh, Dariush, 2020. "A simple test for zero multiple correlation coefficient in high-dimensional normal data using random projection," Computational Statistics & Data Analysis, Elsevier, vol. 148(C).
    • Handle: RePEc:eee:csdana:v:148:y:2020:i:c:s0167947320300463
    DOI: 10.1016/j.csda.2020.106955
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    References listed on IDEAS

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    1. Gupta, Somesh Das, 1977. "Tests on multiple correlation coefficient and multiple partial correlation coefficient," Journal of Multivariate Analysis, Elsevier, vol. 7(1), pages 82-88, March.
    2. Shurong Zheng & Dandan Jiang & Zhidong Bai & Xuming He, 2014. "Inference on multiple correlation coefficients with moderately high dimensional data," Biometrika, Biometrika Trust, vol. 101(3), pages 748-754.
    3. Ding, Cherng G., 1996. "On the computation of the distribution of the square of the sample multiple correlation coefficient," Computational Statistics & Data Analysis, Elsevier, vol. 22(4), pages 345-350, August.
    4. Ogasawara, Haruhiko, 2006. "Asymptotic expansion of the sample correlation coefficient under nonnormality," Computational Statistics & Data Analysis, Elsevier, vol. 50(4), pages 891-910, February.
    5. Benton, Denise & Krishnamoorthy, K., 2003. "Computing discrete mixtures of continuous distributions: noncentral chisquare, noncentral t and the distribution of the square of the sample multiple correlation coefficient," Computational Statistics & Data Analysis, Elsevier, vol. 43(2), pages 249-267, June.
    6. Liang, Jiajuan & Tang, Man-Lai & Chan, Ping Shing, 2009. "A generalized Shapiro-Wilk W statistic for testing high-dimensional normality," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3883-3891, September.
    7. Tan, Ming & Fang, Hong-Bin & Tian, Guo-Liang & Wei, Gang, 2005. "Testing multivariate normality in incomplete data of small sample size," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 164-179, March.
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