A two-sample test for high-dimensional data with applications to gene-set testing

By Songxi Chen, Yingli Qin. 2010

629 citations recorded by the source corpus.

We proposed a two sample test for means of high dimensional data when the data dimension is much larger than the sample size. The classical Hotelling's $T^2$ test does not work for this ``large p, small n" situation. The proposed test does not require explicit conditions on the relationship between the data dimension and sample size. This offers much flexibility in analyzing high dimensional data. An application of the proposed test is in testing significance for sets of genes, which we demonstrate in an empirical study on a Leukemia data set.

Subfields: Molecular Biology

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Citations in the corpus

Adaptivity and Computation-Statistics Tradeoffs for Kernel and Distance based High Dimensional Two Sample Testing (2015, background): “In another extension of TBS by Chen and Qin [2010], henceforth called CQ, the authors proposed a variant of TBS of the form”
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).”
On testing the equality of high dimensional mean vectors with unequal covariance matrices (2014, methodology): “However, for each sub-hypothesis, there is a test statistic of Chen and Qin (2010).”
Identifying Cointegration by Eigenanalysis (2015, background): “As expected, the estimation errors decrease as sample size n increases, and the errors with (p, r, s) = (10, 4, 4) are greater than those with (p, r, s) = (6, 2, 2).”
Uniform change point tests in high dimension (2015, neutral): “ion with panel data or factor models. For example, in [16], various sparsity constraints are discussed to introduce the IVAR (inﬁnitedimensional vector-autoregression). Other approaches are oﬀered in [13, 15]. Here, we will ﬁrst follow the approach taken in the latter, before coming back to (5.1). L”
Outlier detection for high-dimensional data (2015, background): “This drawback has also been revealed by some high-dimensional location tests (Srivastava & Du, 2008; Chen & Qin, 2010).”
A More Powerful Two-Sample Test in High Dimensions using Random Projection (2011, positive): “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.”
Two-sample tests for high-dimension, strongly spiked eigenvalue models (2016, background): “In such situations, Dempster (1958, 1960) and Srivastava (2007) considered the test when π1 and π2 are Gaussian. When π1 and π2 are non-Gaussian, Bai and Saranadasa (1996) and Cai, Liu, and Xia (2014) considered the test under homoscedasticity, Σ1 = Σ2.”
Two Sample Tests for High Dimensional Covariance Matrices (2012, methodology): “The da-TWO Chen and Qin (2010) for analysis on the same dataset.”
Tests alternative to higher criticism for high-dimensional means under sparsity and column-wise dependence (2013, background): “Hall and Jin (2008) and Delaigle and Hall (2009) studied the detection boundary for dependent data and Cai and Wu (2012) studied the boundary for detecting mixtures with a general known distribution.”
Two-Stage Procedures for High-Dimensional Data (2011, methodology): “They implemented the procedure for two microarray data sets: Leukemia (n = 72, n1 = 47, n2 = 25, p = 7129) in Golub et al. (1999) and Colon cancer data (n = 62, n1 = 22, n2 = 40, p = 2000) in Alon et al.”
Jackknife Empirical Likelihood Test for Equality of Two High Dimensional Means (2013, positive): “, 1)T ∈ Rd and the test in Chen and Qin (2010), at level 5%. Results for level 10% are similar. From the tables we observe that the sizes of both tests are comparable and quite stable with respect to the dimension d; the proposed jackknife empirical likelihood test is more powerful than the test in ”
Two‐sample test of high dimensional means under dependence (2014, methodology): “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…”
RAPTT: An Exact Two-Sample Test in High Dimensions Using Random Projections (2014, methodology): “The modified statistic proposed by Chen and Qin (2010) is CQ = ∑ i =j XiX ′ j n1(n1−1) + ∑ i =j YiY ′ j n1(n1−1) − 2 ∑n1 i=1 ∑n2 j=1 XiY ′ j n1n2 σ̂n , where σ̂n is an estimate of the standard error of the numerator.”