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

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Najarzadeh D.

مرکز اطلاعات علمی Scientific Information Database (SID) - Trusted Source for Research and Academic Resources

Journal Paper

Paper Information

Journal: JOURNAL OF STATISTICAL SCIENCES Year:2023 | Volume:17 | Issue:1 Page(s): 201-218

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Information Journal Paper

Title

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

Author(s)

Najarzadeh D. | Issue Writer Certificate

Keywords

Multiple correlation coefficient

High-dimensional normal data

Sparse precision matrix

Plug-in estimator

Permutation test

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.

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