Testing of multivariate repeated measures data with block exchangeable covariance structure

Ivan Žežula, Daniel Klein and Anuradha Roy ()
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Ivan Žežula: P. J. Šafárik University
Daniel Klein: P. J. Šafárik University
Anuradha Roy: The University of Texas at San Antonio

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2018, vol. 27, issue 2, No 6, 360-378

Abstract: Abstract A new hypothesis testing of equality of mean vectors in two populations using $$D^2$$ 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 $$q +1$$ q + 1 , unlike $$pq +1$$ p q + 1 in Hotelling’s $$T^2$$ T 2 test. The new test is very efficient in small sample scenario, when the number of observations is not adequate to estimate the $$pq \times pq$$ p q × p q dimensional unknown unstructured variance–covariance matrix. Some simulation studies are performed to compare the power of the new $$D^2$$ D 2 test and the existing $$BT^2$$ B T 2 test. The performance of the proposed $$D^2$$ D 2 test is demonstrated with the two medical data sets.

Keywords: $$BT^2$$ B T 2 statistic; $$D^2$$ D 2 statistic; Hotelling’s $$T^2$$ T 2 statistic; Lawley–Hotelling trace distribution; 62H12; 62H15; 62H10; 62E17 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s11749-017-0549-z

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