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A Permutation Test for Multiple Correlation Coefficient in High Dimensional Normal Data
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Dariush Najarzadeh *    |
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Abstract: (695 Views) |
| In multiple regression analysis, the population multiple correlation coefficient (PMCC) is widely used to measure the correlation between a variable and a set of variables. To evaluate the existence or non-existence of this type of correlation, testing the hypothesis of zero PMCC can be very useful. In high-dimensional data, due to the singularity of the sample covariance matrix, traditional testing procedures to test this hypothesis lose their applicability. A simple test statistic was proposed for zero PMCC based on a plug-in estimator of the sample covariance matrix inverse. Then, a permutation test was constructed based on the proposed test statistic to test the null hypothesis. A simulation study was carried out to evaluate the performance of the proposed test in both high-dimensional and low-dimensional normal data sets. This study was finally ended by applying the proposed approach to mice tumour volumes data. |
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| Keywords: Multiple correlation coefficient, High-dimensional normal data, Sparse precision matrix, Plug-in estimator, Permutation test |
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Full-Text [PDF 289 kb]
(531 Downloads)
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Type of Study: Research |
Subject:
Statistical Inference
Received: 2023/02/24 | Accepted: 2023/09/1 | Published: 2023/07/11
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