A Permutation Test for Multiple Correlation Coefficient in High Dimensional Normal Data

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Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:

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.

Language:
Persian
Published:
Journal of Statistical Sciences, Volume:17 Issue: 1, 2023
Pages:
201 to 218
https://www.magiran.com/p2606695