Randomization Tests for a Multivariate Two-Sample Problem

Chung, Janet; Fraser, D. A. S.

doi:10.2307/2282050

Cited by 17 publications

(15 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Tests for the equality of two mean vectors, that is, tests of our H 0 where g = 2, when the number of variables p is large have been developed by Chung and Fraser [5], Dempster [7,8], and Bai and Saranadasa [2]. In particular, Bai and Saranadasa [2] considered the statistic…”

Section: A Test For the Equality Of Mean Vectorsmentioning

confidence: 99%

Some high-dimensional tests for a one-way MANOVA

Schott¹

2007

Journal of Multivariate Analysis

View full text Add to dashboard Cite

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.

show abstract

Section: A Test For the Equality Of Mean Vectorsmentioning

confidence: 99%

Some high-dimensional tests for a one-way MANOVA

Schott¹

2007

Journal of Multivariate Analysis

View full text Add to dashboard Cite

show abstract

“…2.3 to compute T 2 . We propose to combine T 1 and T 2 to test for H 0 : μ X = μ Y and X = Y , and we consider the Tippett type combing function (see Chung and Fraser 1958;Hirotsu 1986Hirotsu , 1998Pesarin 2001). Let λ 1 and λ 2 be the p values of the tests T 1 and T 2 , respectively.…”

Section: Test Statisticsmentioning

confidence: 99%

Distribution-free tests of mean vectors and covariance matrices for multivariate paired data

Lim

Kim

et al. 2011

Metrika

View full text Add to dashboard Cite

We study a permutation procedure to test the equality of mean vectors, homogeneity of covariance matrices, or simultaneous equality of both mean vectors and covariance matrices in multivariate paired data. We propose to use two test statistics for the equality of mean vectors and the homogeneity of covariance matrices, respectively, and combine them to test the simultaneous equality of both mean vectors and covariance matrices. Since the combined test has composite null hypothesis, we control its type I error probability and theoretically prove the asymptotic unbiasedness and consistency of the combined test. The new procedure requires no structural assumption on the covariances. No distributional assumption is imposed on the data, except that the permutation test for mean vector equality assumes symmetric joint distribution of the paired data. We illustrate the good performance of the proposed approach with comparison to competing methods via simulations. We apply the proposed method to testing the symmetry of tooth size in a dental study and to finding differentially expressed gene sets with dependent structures in a microarray study of prostate cancer.123 834 E. Li et al.

show abstract

“…Repeat this procedure until all possible permutations are accounted for. Alternatively, choose a random (Block, 1960;Dwass, 1957) or systematic (Chung & Fraser, 1958) subset of all possible samples that will produce a good approximation of the whole empirical sampling distribution. (Note that, while the description above implies a one-way ANOVA design, Edgington, 1987, describes the generalization of the randomization test to higher-way designs and to correlation and regression settings.…”

Section: The Randomization Testmentioning

confidence: 99%

The Bootstrap, the Jackknife, and the Randomization Test: A Sampling Taxonomy

Rodgers¹

1999

Multivariate Behavioral Research

120

View full text Add to dashboard Cite

A simple sampling taxonomy is defined that shows the differences between and relationships among the bootstrap, the jackknife, and the randomization test. Each method has as its goal the creation of an empirical sampling distribution that can be used to test statistical hypotheses, estimate standard errors, and/or create confidence intervals. Distinctions between the methods can be made based on the sampling approach (with replacement versus without replacement) and the sample size (replacing the whole original sample versus replacing a subset of the original sample). The taxonomy is useful for teaching the goals and purposes of resampling schemes. An extension of the taxonomy implies other possible resampling approaches that have not previously been considered. Univariate and multivariate examples are presented.

show abstract

Randomization Tests for a Multivariate Two-Sample Problem

Cited by 17 publications

References 0 publications

Some high-dimensional tests for a one-way MANOVA

Some high-dimensional tests for a one-way MANOVA

Distribution-free tests of mean vectors and covariance matrices for multivariate paired data

The Bootstrap, the Jackknife, and the Randomization Test: A Sampling Taxonomy

Contact Info

Product

Resources

About