### 抄録

In this paper we propose a test for testing the equality of the mean vectors of two groups with unequal covariance matrices based on N_{1} and N_{2} independently distributed p-dimensional observation vectors. It will be assumed that N_{1} observation vectors from the first group are normally distributed with mean vector μ1 and covariance matrix Σ1. Similarly, the N_{2} observation vectors from the second group are normally distributed with mean vectorμ2 and covariance matrixΣ2.Wepropose a test for testing the hypothesis that μ1 = μ2. This test is invariant under the group of p×p nonsingular diagonal matrices. The asymptotic distribution is obtained as (N_{1}, N_{2}, p) → ∞and N_{1}/(N_{1} + N_{2}) → k ∈ (0, 1) but N_{1}/p and N2/p may go to zero or infinity. It is compared with a recently proposed noninvariant test. It is shown that the proposed test performs the best.

元の言語 | English |
---|---|

ページ（範囲） | 349-358 |

ページ数 | 10 |

ジャーナル | Journal of Multivariate Analysis |

巻 | 114 |

発行部数 | 1 |

DOI | |

出版物ステータス | Published - 2013 1 1 |

外部発表 | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Statistics and Probability
- Numerical Analysis
- Statistics, Probability and Uncertainty

### これを引用

*Journal of Multivariate Analysis*,

*114*(1), 349-358. https://doi.org/10.1016/j.jmva.2012.08.014

**A two sample test in high dimensional data.** / Srivastava, Muni S.; Katayama, Shota; Kano, Yutaka.

研究成果: Article

*Journal of Multivariate Analysis*, 巻. 114, 番号 1, pp. 349-358. https://doi.org/10.1016/j.jmva.2012.08.014

}

TY - JOUR

T1 - A two sample test in high dimensional data

AU - Srivastava, Muni S.

AU - Katayama, Shota

AU - Kano, Yutaka

PY - 2013/1/1

Y1 - 2013/1/1

N2 - In this paper we propose a test for testing the equality of the mean vectors of two groups with unequal covariance matrices based on N1 and N2 independently distributed p-dimensional observation vectors. It will be assumed that N1 observation vectors from the first group are normally distributed with mean vector μ1 and covariance matrix Σ1. Similarly, the N2 observation vectors from the second group are normally distributed with mean vectorμ2 and covariance matrixΣ2.Wepropose a test for testing the hypothesis that μ1 = μ2. This test is invariant under the group of p×p nonsingular diagonal matrices. The asymptotic distribution is obtained as (N1, N2, p) → ∞and N1/(N1 + N2) → k ∈ (0, 1) but N1/p and N2/p may go to zero or infinity. It is compared with a recently proposed noninvariant test. It is shown that the proposed test performs the best.

AB - In this paper we propose a test for testing the equality of the mean vectors of two groups with unequal covariance matrices based on N1 and N2 independently distributed p-dimensional observation vectors. It will be assumed that N1 observation vectors from the first group are normally distributed with mean vector μ1 and covariance matrix Σ1. Similarly, the N2 observation vectors from the second group are normally distributed with mean vectorμ2 and covariance matrixΣ2.Wepropose a test for testing the hypothesis that μ1 = μ2. This test is invariant under the group of p×p nonsingular diagonal matrices. The asymptotic distribution is obtained as (N1, N2, p) → ∞and N1/(N1 + N2) → k ∈ (0, 1) but N1/p and N2/p may go to zero or infinity. It is compared with a recently proposed noninvariant test. It is shown that the proposed test performs the best.

KW - Asymptotic theory

KW - Behrens-Fisher problem

KW - High-dimensional data

KW - Hypothesis testing

UR - http://www.scopus.com/inward/record.url?scp=84867812899&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867812899&partnerID=8YFLogxK

U2 - 10.1016/j.jmva.2012.08.014

DO - 10.1016/j.jmva.2012.08.014

M3 - Article

AN - SCOPUS:84867812899

VL - 114

SP - 349

EP - 358

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

SN - 0047-259X

IS - 1

ER -