【摘 要】
：
Assume we have a sample of size n from a p-dimensional population with first four finite moments. We are interested in testing some basic hypothesis about t
【机 构】
：
University of Tartu,Estonia
【出 处】
：
The 24th International Workshop on Matrices and Statistics(第
论文部分内容阅读
Assume we have a sample of size n from a p-dimensional population with first four finite moments. We are interested in testing some basic hypothesis about the covariance structure in the dispersion matrix Σ. We are concentrating to the sphericity test and the uncorrelatedness test in the situation when both, the sample size and the number of variables can be large. As motivated in Srivastava (2005) we can not rely on maximum likelihood tests in this framework. For the test of sphericity we derive asymptotic expansion of a teststatistic constructed via trace functions of the sample dispersion matrix and find its asymptotic normal distribution under null-hypothesis. For the uncorrelatedness test a chi-square test-statistic is constructed. In a simulation study probabilistic behaviour of these test-statistics is studied and speed of convergence to the asymptotic distributions examined.
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