A test for the mean vector with fewer observations than the dimension

By Muni S. Srivastava, M. Du. 2008

298 citations recorded by the source corpus.

In this paper, we consider a test for the mean vector of independent and identically distributed multivariate normal random vectors where the dimension p is larger than or equal to the number of observations N. This test is invariant under scalar transformations of each component of the random vector. Theories and simulation results show that the proposed test is superior to other two tests available in the literature. Interest in such significance test for high-dimensional data is motivated by DNA microarrays. However, the methodology is valid for any application which involves high-dimensional data.

Subfields: Artificial Intelligence, Molecular Biology

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Citations in the corpus

Interpreting support vector machine models for multivariate group wise analysis in neuroimaging (2015, neutral): “…by our inference framework may be applied to improve the interpretability of neuroimaging based SVM classifier it should not be confused for multivariate statistical testing frameworks like MANOVA Casella and Berger (2002) Srivastava and Du (2008) Fujikoshi et al. (2004) (or its equivalents).”
Adaptivity and Computation-Statistics Tradeoffs for Kernel and Distance based High Dimensional Two Sample Testing (2015, background): “Srivastava and Du [2008] and Srivastava et al. [2013] proposed to instead use diag( S ) − 1 instead of S − 1 , in T H , and showed its advantages in certain settings over T BS (speciﬁcally its scale invariance, i.e. invariance when the data is rescaled by a diagonal matrix, gives it an advantage…”
Two‐sample test of high dimensional means under dependence (2014, unknown): “Srivastava and Du (2008) and Srivastava (2009) constructed test statistics by replacing ï¿¿ Σ −1 with the inverse of the diagonal of ï¿¿ Σ. Chen and Qin (2010) introduced a test statistic by removing the cross-product terms ï¿¿ n 1 i=1 X ï¿¿ i X i and ï¿¿ n 2 i=1 Y ï¿¿ i Y i in ï¿¿ ¯ X − ¯ Y ï¿¿ 2…”
Statistical Query Lower Bounds for Robust Estimation of High-Dimensional Gaussians and Gaussian Mixtures (2016, background): “More recently, testers that succeed in the sublinear regime have been developed [68].”
On testing the equality of high dimensional mean vectors with unequal covariance matrices (2014, background): “ problem in the case of two sample problem. Since then, more high dimensional tests have been proposed by Bai and Saranadasa (1996); Srivastava and Fujikoshi (2006); Srivastava (2007); Schott (2007); Srivastava and Du (2008);Srivastava (2009); Srivastava and Yanagihara (2010); Chen and Qin (2010); S”
Jackknife Empirical Likelihood Test for Equality of Two High Dimensional Means (2013, unknown): “Under conditions of Theorem 1, we have as min{n1, n2} → ∞ √ m m1m2 √ ρ m1 ∑ i=1 X i m2 ∑ j=1 Ȳj p → 0, (16) 1 m1 √ τ m1 ∑ i=1 α Xi p → 0, (17) 12”
A two sample test in high dimensional data (2013, methodology): “This correction term has been given by Srivastava and Du [6] in the connection of a test when the covariance matrices of the two groups are equal.”
RAPTT: An Exact Two-Sample Test in High Dimensions Using Random Projections (2014, background): “Srivastava and Du (2008) considered the statistic where R = diag ( S ) − 12 S diag ( S ) − 12 .”
Random matrix theory in statistics: A review (2014, methodology): “To fix this problem, tests based on certain quadratic functionals of the sample covariance and correlation matrices have been proposed by Chen and Qin (2010) and Srivastava and Du (2008).”
A Simple Two-Sample Test in High Dimensions Based on L2-Norm (2020, methodology): “…considered by Katayama, Kanoa, and Srivastava (2013), Aoshima and Yata (2018), and others, nor it assumes restrictive conditions on the covariance matrix such as (8)–(10) imposed by Bai and Saranadasa (1996), Chen and Qin (2010), and Srivastava and Du (2008), which rarely hold in high dimensions.”
A More Powerful Two-Sample Test in High Dimensions using Random Projection (2011, unknown): “In Section 3.3, we demonstrate an optimality property of the choice k = ⌊ n/ 2 ⌋ , which is valid in moderate or high-dimensions, i.e., p ≥ ⌊ n/ 2 ⌋ , and we restrict our attention to this case in Theorems 2 and 3.”
Multivariate-Sign-Based High-Dimensional Tests for the Two-Sample Location Problem (2016, background): “Consider a simple setting, tr(R2i ) = O(p) (Srivastava and Du 2008).”
TWO-SAMPLE BEHRENS-FISHER PROBLEM FOR HIGH-DIMENSIONAL DATA (2015, methodology): “(i)−(iii) in Srivastava and Du (2008), the test statistic Tn is not biased, μn = o( √ var(Tn)) under H0.”
On the High Dimensional Power of a Linear-Time Two Sample Test under Mean-shift Alternatives (2015, background): “Srivastava & Du (2008) proposed to instead use diag(S) instead of S in TH , and showed its advantages in certain settings over TBS .”