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Likelihood ratio test for partial sphericity in high and ultra-high dimensions

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  • Forzani, Liliana
  • Gieco, Antonella
  • Tolmasky, Carlos

Abstract

We consider, in the setting of p and n large, sample covariance matrices whose population counterparts follow a spiked population model, i.e., with the exception of the first (largest) few, all the population eigenvalues are equal. We study the asymptotic distribution of the partial maximum likelihood ratio statistic and use it to test for the dimension of the population spike subspace. Furthermore, we extend this to the ultra-high-dimensional case, i.e., p>n. A thorough study of the power of the test gives a correction that allows us to test for the dimension of the population spike subspace even for values of the limit of p/n close to 1, a setting where other approaches have proved to be deficient.

Suggested Citation

  • Forzani, Liliana & Gieco, Antonella & Tolmasky, Carlos, 2017. "Likelihood ratio test for partial sphericity in high and ultra-high dimensions," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 18-38.
    • Handle: RePEc:eee:jmvana:v:159:y:2017:i:c:p:18-38
    DOI: 10.1016/j.jmva.2017.04.001
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    References listed on IDEAS

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    3. Passemier, Damien & Yao, Jianfeng, 2014. "Estimation of the number of spikes, possibly equal, in the high-dimensional case," Journal of Multivariate Analysis, Elsevier, vol. 127(C), pages 173-183.
    4. Baik, Jinho & Silverstein, Jack W., 2006. "Eigenvalues of large sample covariance matrices of spiked population models," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1382-1408, July.
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