Multiple Comparisons Among Mean Vectors When the Dimension is Larger Than the Total Sample Size

Hyodo, Masashi; Takahashi, Sho; Nishiyama, Takahiro

doi:10.1080/03610918.2012.762387

Cited by 12 publications

(9 citation statements)

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“…This study gives an extension of the results by Hyodo et al (2013) to the unbalanced case. We show that the consistency and asymptotic normality of D ij in (1) and D 1j in (2) remain valid for the unbalanced case.…”

Section: Introductionmentioning

confidence: 99%

“…In order to get a corrected estimator of this percentile, we derive the CornishFisher expansion of z 1·p . This expansion is derived in Hyodo et al (2013) in the balanced case. In a similar manner, we can show that the result of Hyodo et al (2013) is applicable to the unbalanced case.…”

Section: Pairwise Comparisonsmentioning

confidence: 99%

“…This expansion is derived in Hyodo et al (2013) in the balanced case. In a similar manner, we can show that the result of Hyodo et al (2013) is applicable to the unbalanced case. Thus, under the high-dimensional asymptotic frameworks A1 and A2, we can obtain the following approximation for z 1·p in the unbalanced case:…”

Section: Pairwise Comparisonsmentioning

confidence: 99%

“…We show that the consistency and asymptotic normality of D ij in (1) and D 1j in (2) remain valid for the unbalanced case. For the procedures derived in Hyodo et al (2013), the coverage probability can be controlled provided the assumption that the data are normally distributed. However, so far no satisfactory test is available to ascertain the multivariate normality of the data when N i ≤ p. Hence, it would be desirable to derive such multiple comparison procedures for which the coverage probability can be controlled with or without the assumption of normality of the data, that is, their procedures are robust under nonnormality.…”

Section: Introductionmentioning

confidence: 99%

“…

ABSTRACTThis paper analyzes whether procedures for multiple comparison derived in Hyodo et al (2013) work for an unbalanced case and under non-normality. We focus on pairwise multiple comparisons and comparisons with a control among mean vectors, and show that the asymptotic properties of these procedures remain valid in an unbalanced high-dimensional setting.

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mentioning

confidence: 99%

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MULTIPLE COMPARISON PROCEDURES FOR HIGH-DIMENSIONAL DATA AND THEIR ROBUSTNESS UNDER NON-NORMALITY

Takahashi

Hyodo

Nishiyama

et al. 2013

Journal of the Japanese Society of Computational Statistics

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This paper analyzes whether procedures for multiple comparison derived in Hyodo et al. (2013) work for an unbalanced case and under non-normality. We focus on pairwise multiple comparisons and comparisons with a control among mean vectors, and show that the asymptotic properties of these procedures remain valid in an unbalanced high-dimensional setting. We also numerically justify that the derived procedures are robust under non-normality, i.e., the coverage probability of these procedures can be controlled with or without the assumption of normality of the data.

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Section: Introductionmentioning

confidence: 99%

Section: Pairwise Comparisonsmentioning

confidence: 99%