Inference on High-Dimensional Mean Vectors with Fewer Observations Than the Dimension

Kazuyoshi Yata () and Makoto Aoshima ()
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Kazuyoshi Yata: University of Tsukuba
Makoto Aoshima: University of Tsukuba

Methodology and Computing in Applied Probability, 2012, vol. 14, issue 3, 459-476

Abstract: Abstract We focus on inference about high-dimensional mean vectors when the sample size is much fewer than the dimension. Such data situation occurs in many areas of modern science such as genetic microarrays, medical imaging, text recognition, finance, chemometrics, and so on. First, we give a given-radius confidence region for mean vectors. This inference can be utilized as a variable selection of high-dimensional data. Next, we give a given-width confidence interval for squared norm of mean vectors. This inference can be utilized in a classification procedure of high-dimensional data. In order to assure a prespecified coverage probability, we propose a two-stage estimation methodology and determine the required sample size for each inference. Finally, we demonstrate how the new methodologies perform by using a microarray data set.

Keywords: Classification; Confidence region; HDLSS; Sample size determination; Two-stage estimation; Variable selection; 62L10; 62H10 (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11009-011-9233-z

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