## Testing of multivariate repeated measures data with block exchangeable covariance structure.(English)Zbl 1404.62062

Summary: A new hypothesis testing of equality of mean vectors in two populations using $$D^2$$ statistic for multivariate repeated measures data on $$q$$ response variables at $$p$$ sites or time points in a block exchangeable covariance matrix setting is proposed. The minimum sample size needed for our new test is only $$q +1$$, unlike $$pq +1$$ in Hotelling’s $$T^2$$ test. The new test is very efficient in small sample scenario, when the number of observations is not adequate to estimate the $$pq \times pq$$ dimensional unknown unstructured variance-covariance matrix. Some simulation studies are performed to compare the power of the new $$D^2$$ test and the existing $$BT^2$$ test. The performance of the proposed $$D^2$$ test is demonstrated with the two medical data sets.

### MSC:

 62H15 Hypothesis testing in multivariate analysis 62H12 Estimation in multivariate analysis 62H10 Multivariate distribution of statistics 62E17 Approximations to statistical distributions (nonasymptotic) 62P10 Applications of statistics to biology and medical sciences; meta analysis
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