Testes computacionalmente intensivos e assintóticos robustos para estrutura de simetria composta

Abstract

The covariance matrix with a compound symmetry structure is used in many statistical proce- dures, as in experimentation when the experiment is carried out with plots repeated in time, in

mixed linear or non-linear models, as well as in genetic studies. To make inferences about the compound symmetry structure the hypothesis test based on the ratio of the maximum likelihood functions is commonly used. This test has as its main limitation the complexity of establishing a distribution for test statistics under the null hypothesis. For this, an asymptotic distribution is used for statistics of the test, in addition to assuming multivariate normality of the sample data, making it a weak test when this condition is violated. Therefore, the objective of this work is to propose three robust tests in the presence of deviations from normality caused by outliers, the first being an asymptotic test based on robust estimators (LRTR), the second, a computationally intensive test based on robust estimators (BLRTR) and the third, a computationally intensive test based on classical estimators (BLTRO). Comparing the performances of the three proposed tests with the original likelihood ratio test (LRTO) and with the robust test (MCPT) created by

Morris, Payton e Santorico (2011). In addition to verifying that the tests that used the robust Co- median estimators, LRTR and BLRTR, obtained better performances than the LRTO, BLRTO

and MCPT tests when considering deviations from normality of data caused by outliers, as well as in the ideal scenario of normally distributed data. The tests were evaluated using the type I error rate and power, in Monte Carlo simulations. It is concluded that the robust estimators did not add improvements to the asymptotic tests or to the computationally intensive tests. The

BLRTO and BLRTR tests performed better than the LRTO, LRTR and MCPT tests. There- fore, the BLRTR and BLRTO tests outperformed the original likelihood ratio test in two ways:

they control the type I error rate when there are outliers in the data and do not use asymptotic distribution for test statistics.