Abstract
Jennrich statistic is a method that can be used to test the equality of 2 or more independent correlation matrices. However, Jennrich statistic begins to be problematic when there is presence of outliers that could lead to invalid results. When exiting outliers in data, Jennrich statistic implications will affect Type I errors and will reduce the power of test. To overcome the presence of outliers, this study suggests the use of robust methods as an alternative method and therefore, it will integrate the estimator into Jennrich statistic. Thus, it can improve the testing performance of correlation matrix hypotheses in relation to outlier problems. Therefore, this study proposes 3 statistical tests, namely Js-statistic, Jm-statistic, and Jmad-statistic that can be used to test the equation of 2 or more correlation matrices. The performance of the proposed method is assessed using the power of test. The results show that Jm-statistic and Jmad-statistic can overcome outlier problems into Jennrich statistic in testing the correlation matrix hypothesis. Jmad-statistic is also superior in testing the correlation matrix hypothesis for different sample sizes, especially those involving 10% outliers.
Highlights
In statistical analysis, testing several correlation matrices play a vital role to measure the linear relationship between different set of groups
The importance of equality of several correlation matrices has been shown in many areas such as economics, financial market, medicine, and social science [7]
Jennrich statistic is a method for testing the equality of 2 or more independent samples correlation matrices [12]–[14]
Summary
In statistical analysis, testing several correlation matrices play a vital role to measure the linear relationship between different set of groups. Jennrich statistic is a method for testing the equality of 2 or more independent samples correlation matrices [12]–[14] This test is constructed based on the likelihood ratio test proposed by Kullback (1967) [9] and it is applied to a sequence of independent samples of correlation matrix based on samples from multivariate normal distribution [15]. This statistic has much better computational and distributional properties [16]
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