## 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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### References:

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