TWO-SAMPLE BEHRENS-FISHER PROBLEM FOR HIGH-DIMENSIONAL DATA
TWO-SAMPLE BEHRENS-FISHER PROBLEM FOR HIGH-DIMENSIONAL DATA
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高维数据的两样本 Behrens-Fisher 问题
DOI：
10.5705/ss.2014.048
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发表时间：
2015
影响因子：
1.4
通讯作者：
Zhu Lixing
中科院分区：
文献类型：
--
作者：
Feng Long;Zou Changliang;Wang Zhaojun;Zhu Lixing
本文关注高维设置中的两样本 Behrens-Fisher 问题。提出了一种新颖的检验，该检验在某些温和条件下是尺度不变的、渐近正态的，并且允许维数在不同场景下分别从样本量的平方到立方体以速率增长。我们解释了对现有尺度不变检验进行偏差校正的必要性，否则即使在零假设下它们也没有明确定义的限制。我们还给出了一些例子，从理论上证明当两个样本的方差不同时，尺度不变检验相对于尺度变异检验的优势。本文关注高维设置中的两样本 Behrens-Fisher 问题。假设 {Xi1; · · · ;Xini } for i = 1; 2 是大小为 n1 和 n2 的两个独立随机样本，来自位于 p 变量中心 1 和 2 的 p 变量分布 F (x − 1) 和 G(x − 2)。表示 n = n1 + n2。我们希望测试是在两个协方差相等的情况下开发的，例如 1 = 2 = 。 Bai和Saranadasa建议的关键特征是使用欧几里得范数代替马哈拉诺比斯范数，因为当p=n → c > 0时，样本协方差矩阵的逆矩阵不再有利。Zhang和Xu (2009)将该方法扩展到k样本高维Behrens-Fisher问题，并导出了当p=n → c < 1时检验统计量的渐近分布。
This article is concerned with the two-sample Behrens-Fisher problem in high-dimensional settings. A novel test is proposed that is scale-invariant, asymp- totically normal under certain mild conditions, and the dimensionality is allowed to grow in the rate, respectively, from square to cube of the sample size in different sce- narios. We explain the necessity of bias correction for existing scale-invariant tests, otherwise they do not have well-defined limits even under the null hypothesis. We also give some examples to theoretically show the advantage of the scale-invariant test over scale-variant tests when variances of the two samples are different. This article is concerned with the two-sample Behrens-Fisher problem in high-dimensional settings. Assume that {Xi1; · · · ;Xini } for i = 1; 2 are two independent random samples with the sizes n1 and n2, from p-variate distribu- tions F (x − 1) and G(x − 2) located at p-variate centers 1 and 2. Denote n = n1 + n2. We wish to test is developed under the equality of the two covariances, say 1 = 2 = . The key feature of the Bai and Saranadasa's proposal is to use the Euclidian norm to replace the Mahalanobis norm since having the inverse of the sample covariance matrix is no longer beneficial when p=n → c > 0. Zhang and Xu (2009) extended this method to the k-sample high-dimensional Behrens-Fisher problem and derived the asymptotic distribution of the test statistic when p=n → c < 1.
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影响因子：
2
作者：
Junyong Park;D. Ayyala
通讯作者：
Junyong Park;D. Ayyala
影响因子：
1.9
作者：
R. Fisher
通讯作者：
R. Fisher
影响因子：
2.7
作者：
Ying Yao
通讯作者：
Ying Yao
相关性下高维均值的两样本检验
DOI：
10.1111/rssb.12034
发表时间：
2014-03-01
影响因子：
5.8
作者：
Cai, T. Tony;Liu, Weidong;Xia, Yin
通讯作者：
Xia, Yin
影响因子：
2.7
作者：
S. Johansen
通讯作者：
S. Johansen