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Title: Inference on mean vectors for high-dimensional data with the strongly spiked eigenstructure Authors:  Aki Ishii - Tokyo University of Science (Japan) [presenting]
Kazuyoshi Yata - University of Tsukuba (Japan)
Makoto Aoshima - University of Tsukuba (Japan)
Abstract: Constructing theories and methodologies for high-dimensional data has become increasingly important in many fields. It is known that high-dimensional data include strongly spiked noise and the noise is troublesome when we analyze high-dimensional data. A lot of conventional methods are heavily influenced by such huge noise and cannot claim accuracy. We note that such huge noise generates a strongly spiked eigenstructure. In order to remove the strongly spiked noise, a data transformation technique has been previously developed. First, we consider one-sample test by using the data transformation. We construct a new test procedure and show that our test procedure works well both in theory and simulation. We also apply the test procedure to multisample problem. Finally, we give some demonstrations by using famous microarray data sets.