| Title: | High-Dimensional Tests for Two Population Mean Vectors |
|---|---|
| Description: | Tests for two high-dimensional population mean vectors. The user has the option to compute the asymptotic, the permutation or the bootstrap based p-value of the test. Some references are: Chen S.X. and Qin Y.L. (2010). <doi:10.1214/09-AOS716>, Cai T.T., Liu W., and Xia Y. (2014) <doi:10.1111/rssb.12034> and Yu X., Li D., Xue L. and Li, R. (2023) <doi:10.1080/01621459.2022.2061354>. |
| Authors: | Michail Tsagris [aut, cre], Manos Papadakis [aut] |
| Maintainer: | Michail Tsagris <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.0 |
| Built: | 2024-11-20 06:23:04 UTC |
| Source: | CRAN |
The package contains a few tests for the case of two high-dimensional population mean vectors. The user has the option to compute the asymptotic, the permutation or the bootstrap based p-value of the test.The tests are based on three other packages, namely the highmean, highDmean and the PEtests. We took the codes, modified them and made them more efficient.
| Package: | highd2means |
| Type: | Package |
| Version: | 1.0 |
| Date: | 2024-08-17 |
| License: | GPL-2 |
Michail Tsagris [email protected].
Michail Tsagris [email protected] and Manos Papadakis [email protected].
Bai Z.D. and Saranadasa H. (1996). Effect of high dimension: by an example of a two sample problem. Statistica Sinica, 6(2): 311–329.
Cai T.T., Liu W., and Xia Y. (2014). Two-sample test of high dimensional means under dependence. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 76(2): 349–372.
Chen S.X. and Qin Y.L. (2010). A two-sample test for high-dimensional data with applications to gene-set testing. The Annals of Statistics, 38(2) 808–835.
Chen S.X., Li J., and Zhong P.S. (2014). Two-Sample Tests for High Dimensional Means with Thresholding and Data Transformation. arXiv preprint arXiv:1410.2848.
Srivastava M.S. and Du M. (2008). A test for the mean vector with fewer observations than the dimension. Journal of Multivariate Analysis, 99(3): 386–402.
Srivastava, M.S., Katayama, S., and Kano, Y. (2013). A two sample test in high dimensional data. Journal of Multivariate Analysis, 114: 349–358.
Yu X., Li D., Xue L. and Li, R. (2023). Power-enhanced simultaneous test of high-dimensional mean vectors and covariance matrices with application to gene-set testing. Journal of the American Statistical Association, 118(544): 2548–2561.
High-dimensional tests for 2 population mean vectors.
means.test(x1, x2, test = "baisara", cov.equal = TRUE, Rp = 1, Rb = 1, ncores = 1)means.test(x1, x2, test = "baisara", cov.equal = TRUE, Rp = 1, Rb = 1, ncores = 1)
x1 |
A numerical matrix with data, where the number of columns (variables) is greater than the number of rows (observations). |
x2 |
A numerical matrix with data, where the number of columns (variables) is greater than the number of rows (observations). |
test |
The test to run. "baisara" corresponds to the test proposed by Bai and Saranadasa (1996), "cailiuxia" to the test proposed by Cai, Liu and Xia (2014), "chenlizho" to the test proposed by Chen, Li and Zhong (2014), "chenqin" to the test proposed by Chen and Qin (2010), and "sridu" to the test proposed by Srivastava and Du (2008). Finally, the "skk" corresponds to the test proposed by Srivastava, Katayama, and Kano(2013). |
cov.equal |
This argument applies to the "cailiuxia", "chenlizho" and "chenqin" tests only. If this is true, it assumes that the two population covariance matrices are equal. |
Rp |
The number of permutations to perform. |
Rb |
The number of bootstrap samples to draw. |
ncores |
The number of cores to use. By default is 1, so no parallel computations take place. You are advised to load the necessary libraries prior to using this argument. |
These methods are designed for high-dimensional data. If the data dimension is smaller than 30 this may result in an inflated Type-I error rate.
Note that these tests were taken from the highmean package, except for the "skk" which was taken from the highDmean package. The "cailiaxiu" and "chenqin" tests here should be the same as in the function pe.test ("clx" and "cq", respectively), but the authors of that package and of the package highmean give different formulas.
A list including:
stat |
The test statistic value. |
pvalue |
The asymptotic p-value of the test. |
perm.pvalue |
The permutation based p-value will appear only if the argument Rp is greater than 1. |
boot.pvalue |
The bootstrap based p-value will appear only if the argument Rp is greater than 1. |
Michail Tsagris and Manos Papadakis.
R implementation and documentation: Michail Tsagris [email protected] and Manos Papadakis [email protected].
Bai Z.D. and Saranadasa H. (1996). Effect of high dimension: by an example of a two sample problem. Statistica Sinica, 6(2): 311–329.
Cai T.T., Liu W., and Xia Y. (2014). Two-sample test of high dimensional means under dependence. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 76(2): 349–372.
Chen S.X. and Qin Y.L. (2010). A two-sample test for high-dimensional data with applications to gene-set testing. The Annals of Statistics, 38(2) 808–835.
Chen S.X., Li J., and Zhong P.S. (2014). Two-Sample Tests for High Dimensional Means with Thresholding and Data Transformation. arXiv preprint arXiv:1410.2848.
Srivastava M.S. and Du M. (2008). A test for the mean vector with fewer observations than the dimension. Journal of Multivariate Analysis, 99(3): 386–402.
Srivastava, M.S., Katayama, S., and Kano, Y. (2013). A two sample test in high dimensional data. Journal of Multivariate Analysis, 114: 349–358.
n1 <- 50 ; n2 <- 100 ; p <- 500 x1 <- matrix( rnorm(n1 * p), nrow = n1, ncol = p) x2 <- matrix( rnorm(n2 * p), nrow = n2, ncol = p) means.test(x1, x2)n1 <- 50 ; n2 <- 100 ; p <- 500 x1 <- matrix( rnorm(n1 * p), nrow = n1, ncol = p) x2 <- matrix( rnorm(n2 * p), nrow = n2, ncol = p) means.test(x1, x2)
Power-enhanced high-dimensional tests for 2 population mean vectors.
pe.test(x1, x2, test = "clx", Rp = 1, Rb = 1, ncores = 1)pe.test(x1, x2, test = "clx", Rp = 1, Rb = 1, ncores = 1)
x1 |
A numerical matrix with data, where the number of columns (variables) is greater than the number of rows (observations). |
x2 |
A numerical matrix with data, where the number of columns (variables) is greater than the number of rows (observations). |
test |
The test to run, either "clx" corresponding to the test proposed by Cai, Liu and Xia (2014), "cq" corresponding to the test proposed by Chen and Qin (2010). The "pecf" combines the two previous methods using the Cauchy and the Fisher approaches. The "pecomp" updates the "cq" test via the power-enhanced component. |
Rp |
The number of permutations to perform. This is applicable only for the "clx" and "cq" tests. |
Rb |
The number of bootstrap samples to draw. This is applicable only for the "clx" and "cq" tests. |
ncores |
The number of cores to use. By default is 1, so no parallel computations take place. You are advised to load the necessary libraries prior to using this argument. |
These methods are designed for high-dimensional data. If the data dimension is smaller than 30 this may result in an inflated Type-I error rate.
Note that these tests were taken from the PEtests package. The "clx" and "cq" tests here should be the same as in the function means.test ("cailiaxiu" and "chenqin", respectively), but the authors of that package and of the package highmean give different formulas.
If the test is "clx", "cq" or "pecomp" a list including:
stat |
The test statistic value. |
pvalue |
The asymptotic p-value of the test. |
perm.pvalue |
The permutation based p-value will appear only if the argument Rp is greater than 1. |
boot.pvalue |
The bootstrap based p-value will appear only if the argument Rp is greater than 1. |
If the test is "pecf" a list including:
cq |
A list with the results of the "cq" test, the stat and the pvalue. |
clx |
A list with the results of the "clx" test, the stat and the pvalue. |
pecauchy |
A list with the results of the Cauchy combination, the stat and the pvalue. |
pefisher |
A list with the results of the Fisher combination, the stat and the pvalue. |
Michail Tsagris and Manos Papadakis.
R implementation and documentation: Michail Tsagris [email protected] and Manos Papadakis [email protected].
Cai T.T., Liu W., and Xia Y. (2014). Two-sample test of high dimensional means under dependence. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 76(2): 349–372.
Chen S.X. and Qin Y.L. (2010). A two-sample test for high-dimensional data with applications to gene-set testing. The Annals of Statistics, 38(2) 808–835.
Yu X., Li D., Xue L. and Li, R. (2023). Power-enhanced simultaneous test of high-dimensional mean vectors and covariance matrices with application to gene-set testing. Journal of the American Statistical Association, 118(544): 2548–2561.
n1 <- 50 ; n2 <- 100 ; p <- 500 x1 <- matrix( rnorm(n1 * p), nrow = n1, ncol = p) x2 <- matrix( rnorm(n2 * p), nrow = n2, ncol = p) pe.test(x1, x2, test = "pecf")n1 <- 50 ; n2 <- 100 ; p <- 500 x1 <- matrix( rnorm(n1 * p), nrow = n1, ncol = p) x2 <- matrix( rnorm(n2 * p), nrow = n2, ncol = p) pe.test(x1, x2, test = "pecf")