Power-enhanced high-dimensional tests for 2 population mean vectors {highd2means}R Documentation

Power-enhanced high-dimensional tests for 2 population mean vectors

Description

Power-enhanced high-dimensional tests for 2 population mean vectors.

Usage

pe.test(x1, x2, test = "clx", 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, 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.

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 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.

Value

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.

Author(s)

Michail Tsagris and Manos Papadakis.

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

References

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.

See Also

means.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)
pe.test(x1, x2, test = "pecf")

[Package highd2means version 1.0 Index]