High-dimensional general linear hypothesis testing under heteroscedasticity

Zhou, Bu; Guo, Jia; Zhang, Jin‐Ting

doi:10.1016/j.jspi.2017.03.005

Cited by 29 publications

(9 citation statements)

References 35 publications

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“…From literary review, we found that solution due to Krishnamoorthy and Yu (2004) has the attained significance level close to the nominal significance level satisfactorily, Krishnamoorthy and Xia (2006) among others showed via intensive simulation studies that this test performs best among the approximation solutions to the multivariate Behrens-Fisher problem (Zhou, 2016). Krishnamoorthy and Yu (2004) has been shown to have approximately distribution of 2 T as Fdistribution is given by:…”

Section: Introductionmentioning

confidence: 88%

“…When the sample is being collected more and more, the first direction of the statistical methods will focus about asymptotic optimality of statistical methods. In the other direction, when variables or dimensions of data are being considered increasingly, the focus of statistical analysis shifted from the univariate to multivariate (Zhou, 2016). However, in many practical applications of modern multivariate statistical methods often found a data sets which are much larger number of measurements than the sample size.…”

Section: Introductionmentioning

confidence: 99%

“…In high-dimensional data, for one population when the data has the number of variable exceed sample size (minus 1), p > n i -1, for example the data that collects from DNA microarrays technology where a large number of gene expression levels may be in the hundreds or thousands, are measured on relatively few subjects (Zhou et al, 2017), then the sample covariance matrix S i lose its full rank and will be singular, which makes S i does not have an inverse (Chongcharoen, 2011). Furthermore, for two populations when the data has the number of variable is larger than the sum of the sample sizes (minus 2), p > n 1 + n 2 -2, then the sample covariance matrix S ɶ in (7) does not have an inverse.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Test on the Multivariate Behrens–Fisher Problem in High–Dimensional Data by Block Covariance Estimation

Sukcharoen¹,

Chongcharoen²

2019

Journal of Mathematics and Statistics

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In this paper, we proposed a new testing statistic for testing the equality of mean vectors from two multivariate normal populations when the covariance matrices are unknown and unequal in high-dimensional data. A new test is proposed based on the idea of keeping more information from the sample covariance matrices as much as possible. A proposed test is invariant under scalar transformations and location shifts. We showed that the asymptotic distribution of proposed statistic is standard normal distribution when number of random variables approach infinity. We also compared the performance of the proposed test with other three existing tests by the simulation study. The simulation results showed that the attained significance level of proposed test close to setting nominal significance level satisfactorily. The attained power of proposed test outperforms as the other comparative tests under form of covariance matrices considered which can be arranged to block diagonal matrix structure. The attained power becomes more powerful when the dimension increases for a given sample size or vice versa, or relationship level between random variables in each sample increases. Finally, the proposed test is also illustrated with an analysis of DNA microarray data.

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Section: Introductionmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Test on the Multivariate Behrens–Fisher Problem in High–Dimensional Data by Block Covariance Estimation

Sukcharoen¹,

Chongcharoen²

2019

Journal of Mathematics and Statistics

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“…This approach was pioneered in Bai and Saranadasa (1996) and further developed in Chen and Qin (2010). Various extensions to oneway MANOVA (Srivastava and Fujikoshi, 2006;Yamada and Himeno, 2015;Srivastava and Fujikoshi, 2006;Hu et al, 2017) and a general multi-sample Behrens-Fisher problem under heteroscedasticity (Zhou et al, 2017) exist. Other notable works for the two-sample problem include Biswas and Ghosh et al (2016); Wang et al (2015).…”

Section: Introductionmentioning

confidence: 99%

High-dimensional general linear hypothesis tests via non-linear spectral shrinkage

Li¹,

Aue²,

Paul³

2018

Preprint

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We are interested in testing general linear hypotheses in a high-dimensional multivariate linear regression model. The framework includes many well-studied problems such as two-sample tests for equality of population means, MANOVA and others as special cases. A family of rotationinvariant tests is proposed that involves a flexible spectral shrinkage scheme applied to the sample error covariance matrix. The asymptotic normality of the test statistic under the null hypothesis is derived in the setting where dimensionality is comparable to sample sizes, assuming the existence of certain moments for the observations. The asymptotic power of the proposed test is studied under various local alternatives. The power characteristics are then utilized to propose a data-driven selection of the spectral shrinkage function. As an illustration of the general theory, we construct a family of tests involving ridge-type regularization and suggest possible extensions to more complex regularizers. A simulation study is carried out to examine the numerical performance of the proposed tests.

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“…Statistic T Sc is a representative of the so-called sum-of-squares type statistics as it is based on an estimation of squared Euclidean norm k i=1 n i θ i − θ 2 , whereθ = N −1 k i=1 n i θ i . See Srivastava and Kubokawa (2013), Yamada and Himeno (2015), Hu et al (2017), Zhang et al (2017), Zhou et al (2017) and Cao et al (2019) for some other sum-of-squares type test statistics for general k ≥ 2. It is known that the sum-of-squares type tests are particularly powerful against dense alternatives.…”

mentioning

confidence: 99%

Least Favorable Direction Test for Multivariate Analysis of Variance in High Dimension

Wang¹,

Xu²

2021

STAT SINICA

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This paper considers the problem of multivariate analysis of variance for normal samples in the high dimension medium sample size setting. When the sample dimension is larger than the sample size, the classical likelihood ratio test is not defined since the likelihood function is unbounded. Based on the unboundedness of the likelihood function, we propose a new test called the least favorable direction test. The asymptotic distributions of the test statistic are derived under both nonspiked and spiked covariances. The local asymptotic power function of the test is also given. The asymptotic power function and simulations show that the proposed test is particularly powerful under spiked covariance.

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High-dimensional general linear hypothesis testing under heteroscedasticity

Cited by 29 publications

References 35 publications

A Test on the Multivariate Behrens–Fisher Problem in High–Dimensional Data by Block Covariance Estimation

A Test on the Multivariate Behrens–Fisher Problem in High–Dimensional Data by Block Covariance Estimation

High-dimensional general linear hypothesis tests via non-linear spectral shrinkage

Least Favorable Direction Test for Multivariate Analysis of Variance in High Dimension

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