Some high-dimensional tests for a one-way MANOVA

By James R. Schott. 2007

92 citations recorded by the source corpus.

A statistic is proposed for testing the equality of the mean vectors in a one-way multivariate analysis of variance. The asymptotic null distribution of this statistic, as both the sample size and the number of variables go to infinity, is shown to be normal. Thus, this test can be used when the number of variables is not small relative to the sample size. In particular, it can be used when the number of variables exceeds the degrees of freedom for error, a situation in which standard MANOVA tests are invalid. A related statistic, also having an asymptotic normal distribution, is developed for tests concerning the dimensionality of the hyperplane formed by the population mean vectors. The finite sample size performances of the normal approximations are evaluated in a simulation study.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d3db6acf13b93ed780421e0383a742260f82dcee

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Z. Bai
2. Songxi Chen
3. Jiang Hu
4. Pingshou Zhong
5. Lixu Zhang
6. Chen Wang
7. Wei Wang
8. Tomasz Górecki

In Statistics and Probability

1. Songxi Chen
2. Z. Bai
3. Jiang Hu
4. Pingshou Zhong
5. Lixu Zhang
6. Chen Wang
7. Wei Wang
8. Tomasz Górecki

Citations in the corpus

• Multivariate analysis of variance for functional data (2017, methodology): “Similarly to the case ofMANOVA tests for multivariate variables [2,46], thematrices E and H will be used in constructing test statistics for (1).”
• Tests for High-Dimensional Covariance Matrices (2010, background): “…in the context of multiple tests as in van der Laan and Bryan (2001), Donoho and Jin (2004), Fan, Hall, and Yao (2007), Kosorok and Ma (2007), and Hall and Jin (2008), or in the context of simultaneous multivariate testing as in Bai and Saranadasa (1996), Schott (2007), and Chen and Qin (2010).”
• On testing the equality of high dimensional mean vectors with unequal covariance matrices (2014, background): “n the case of two sample problem. Since then, more high dimensional tests have been proposed by Bai and Saranadasa (1996); Fujikoshi et al. (2004); Srivastava and Fujikoshi (2006); Srivastava (2007); Schott (2007); Srivastava and Du (2008); Srivastava (2009); Srivastava and Yanagihara (2010); Chen a”