High-dimensional tests for 2 population mean vectors {highd2means}R Documentation

High-dimensional tests for 2 population mean vectors

Description

High-dimensional tests for 2 population mean vectors.

Usage

means.test(x1, x2, test = "baisara", cov.equal = TRUE, Rp = 1, Rb = 1, ncores = 1)

Arguments

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.

Details

These methods are designed for high-dimensional data. If the data dimension p 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.

Value

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.

Author(s)

Michail Tsagris and Manos Papadakis.

R implementation and documentation: Michail Tsagris mtsagris@uoc.gr and Manos Papadakis papadakm95@gmail.com.

References

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.

See Also

pe.test

Examples

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)

[Package highd2means version 1.0 Index]