Robust computationally intensive and asymptotic tests for compound symmetry structure

Abstract

The covariance matrix with compound symmetry structure is used in many statistical procedures, as in repeated measures design, in mixed linear or non-linear models, as well as in genetic studies. For making inferences about the compound symmetry structure, the classic original likelihood ratio test (OLRT) is commonly used. The main limitation of this test is the difficulty of establishing an exact distribution for test statistic under the null hypothesis in addition to assuming multivariate normality of the sample data, which makes the test not very robust when this condition is violated. This work aims to propose three robust tests named LRTR, PBTR, and PBTC, which are based on robust estimators and parametric bootstrap methods. Besides that, we intended to compare the performance of the three proposed tests with the classic OLRT and robust MCPT tests that already exist in the literature. We also wanted to check if the proposed tests that are based on the Comedian robust estimators performed better than the OLRT and PBTC when considering or not outliers in the data. Finally, the performance of asymptotic tests was compared to those that are computationally intensive tests. The tests were evaluated using the type I error rate and power in Monte Carlo simulations. We concluded that the Comedian robust estimators did not add improvements to the asymptotic tests or the computationally intensive tests. The PBTC and PBTR performed better than the OLRT, LRTR, and MCTP. Therefore, the PBTC and PBTR outperformed the classic OLRT and the robust MCPT.