Testing homogeneity of several covariance matrices and multi-sample sphericity for high-dimensional data
2013 (English)Report (Other academic)
A test statistic for testing homogeneity of g 2 covariance matri-ces is presented when the data are assumed multivariate normal and thedimension of the vector, p, may exceed the number of such vectors, ni,i = 1; : : : ; g. U-statistics based unbiased and location-invariant estima-tors are used to dene the test statistic. Further, using the asymptotictheory of U-statistics, the test statistic is shown to follow an approximatenormal distribution. This limiting distribution is based on certain mildassumptions on the traces of the unknown common population covariancematrix. Under the null hypothesis of homogeneity of covariance matrices,the test statistic is further extended to test multi-sample sphericity andidentity of the common covariance matrix.
Place, publisher, year, edition, pages
2013. , 35 p.
Working paper / Department of Statistics, Uppsala University, 2013:1
IdentifiersURN: urn:nbn:se:uu:diva-198999OAI: oai:DiVA.org:uu-198999DiVA: diva2:619117