Testing Hypotheses Of Covariance Structure In Multivariate Data

Abstract

In this paper there is given a new approach for testing hypotheses on the structure of covariance matrices in double multivariate data. It is proved that ratio of positive and negative parts of best unbiased estimators (BUE) provide an F-test for independence of blocks variables in double multivariate models.

Testing Hypotheses About Structure of Parameters in Models With Block Compound Symmetric Covariance Structure

“…The presented results can be also found in Fonseca et al (2018). From Roy et al (2015) we get that matrices:…”

“…Estimators of the parameters of the presented BCS covariance structure model and the data presenting measures of mineral content of bones can be found in Roy et al (2016). The power of the proposed tests for expectation and covariance parameters, in the multivariate case, is compared with well-known tests such as LRT and Roy's test in Fonseca et al (2018) and Zmyślony et al (2018). As a result of the simulation study we can say that in some cases (for some alternatives) the tests proposed in this paper have greater power than LRT and Roy's test.…”

“…As a result of the simulation study we can say that in some cases (for some alternatives) the tests proposed in this paper have greater power than LRT and Roy's test. The same data example, as for the estimation purpose, was used for testing hypotheses for covariance structure in Fonseca et al (2018) and for testing hypotheses about the mean structure in Zmyślony et al (2018).…”

“…Test F for testing hypotheses about elements of Γ Γ Γ 1 , whose statistic was given in (14), was compared with LRT, whose statistic was given in formula (3.3) in Fonseca et al (2018). For both tests, on 5% level of significance, we can conclude that at least one element of Γ Γ Γ 1 is different than 0.…”