Fixed-Width Simultaneous Confidence Intervals for Multinormal Means in Several Intraclass Correlation Models

Aoshima, Makoto; Mukhopadhyay, Nitis

doi:10.1006/jmva.1997.1734

Cited by 7 publications

(1 citation statement)

References 18 publications

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“…There are many literatures related to this problem when p is fixed less than n i . One may refer to Ghosh et al (1997), Aoshima and Mukhopadhyay (1998), Aoshima et al (2002), Aoshima and Takada (2004), Aoshima (2005), Yata and Aoshima (2009a) and Aoshima and Yata (2010) among others in which Stein (1945)-type two-stage procedures were proposed in a typical multivariate context. Especially, Aoshima and Yata (2010) provided a general methodology to make a Stein-type twostage procedure asymptotically second-order consistent for a variety of multivariate inference problems such as multiple comparisons and bioequivalence tests.…”

Section: K;mentioning

confidence: 99%

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

Yata

Aoshima

2011

Methodol Comput Appl Probab

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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.

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