caa a22 4500 605519943 CHVBK 20210128100732.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s11009-013-9370-7 doi (NATIONALLICENCE)springer-10.1007/s11009-013-9370-7 Asymptotic Normality for Inference on Multisample, High-Dimensional Mean Vectors Under Mild Conditions [Elektronische Daten] [Makoto Aoshima, Kazuyoshi Yata] In this paper, we consider the asymptotic normality for various inference problems on multisample and high-dimensional mean vectors. We verify that the asymptotic normality of concerned statistics is proved under mild conditions for high-dimensional data. We show that the asymptotic normality can be justified theoretically and numerically even for non-Gaussian data. We introduce the extended cross-data-matrix (ECDM) methodology to construct an unbiased estimator at a reasonable computational cost. With the help of the asymptotic normality, we show that the concerned statistics given by ECDM can ensure consistency properties for inference on multisample and high-dimensional mean vectors. We give several applications such as confidence regions for high-dimensional mean vectors, confidence intervals for the squared norm and the test of multisample mean vectors. We also provide sample size determination so as to satisfy prespecified accuracy on inference. Finally, we give several examples by using a microarray data set. Springer Science+Business Media New York, 2013 Asymptotic normality nationallicence Confidence region nationallicence Cross-data-matrix methodology nationallicence Large p small n nationallicence Microarray nationallicence Two-stage procedure nationallicence Aoshima Makoto Institute of Mathematics, University of Tsukuba, 305-8571, Ibaraki, Japan aut Yata Kazuyoshi Institute of Mathematics, University of Tsukuba, 305-8571, Ibaraki, Japan aut Methodology and Computing in Applied Probability Springer US; http://www.springer-ny.com 17/2(2015-06-01), 419-439 1387-5841 17:2<419 2015 17 11009 https://doi.org/10.1007/s11009-013-9370-7 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s11009-013-9370-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Aoshima Makoto Institute of Mathematics, University of Tsukuba, 305-8571, Ibaraki, Japan aut NATIONALLICENCE 700 1- Yata Kazuyoshi Institute of Mathematics, University of Tsukuba, 305-8571, Ibaraki, Japan aut NATIONALLICENCE 773 0- Methodology and Computing in Applied Probability Springer US; http://www.springer-ny.com 17/2(2015-06-01), 419-439 1387-5841 17:2<419 2015 17 11009