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Title: Equality tests of high-dimensional covariance matrices with strongly spiked eigenstructures Authors:  Aki Ishii - Tokyo University of Science (Japan) [presenting]
Kazuyoshi Yata - University of Tsukuba (Japan)
Makoto Aoshima - University of Tsukuba (Japan)
Abstract: One of the features of modern data is that the data dimension is extremely high, however, the sample size is relatively low. We call such data HDLSS data. In HDLSS situations, new theories and methodologies are required to develop for statistical inferences. We note that eigenvalues of high-dimensional data grow very rapidly depending on the dimension. There are two types of high-dimensional eigenvalue models: the strongly spiked eigenvalue (SSE) model and the non-SSE (NSSE) model. A lot of works have been done under the NSSE model. We consider equality tests of high-dimensional covariance matrices under the strongly spiked eigenvalue (SSE) model. We create a new test procedure on the basis of the high-dimensional eigenstructure. We find the difference of covariance matrices by dividing the high-dimensional eigenstructure into the first eigenspace and the others. We prove that our proposed test procedure has consistency properties both for the size and power. Finally, we check performances of our test procedure in simulations.