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Testing the equality of mean vectors for paired doubly multivariate observations in blocked compound symmetric covariance matrix setup. (English) Zbl 1329.62251

Summary: In this article we develop a test statistic for testing the equality of mean vectors for paired doubly multivariate observations with \(q\) response variables and \(u\) sites in blocked compound symmetric covariance matrix setting. We obtain a natural extension of the Hotelling’s \(T^2\) statistic, the Block \(T^2\) (B\(T^2\)) statistic, a convolution of two \(T^2\)’s, which uses unbiased estimates of the component matrices of the orthogonally transformed blocked compound symmetric covariance matrix that is present in a data set. The new test statistic is implemented with two real data sets. We compare our findings with the conventional Hotelling’s \(T^2\) statistic.

MSC:

62H10 Multivariate distribution of statistics
62H12 Estimation in multivariate analysis
62H15 Hypothesis testing in multivariate analysis
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