# epval_Bai1996: Empirical Permutation-Based p-value of the Test Proposed by... In highmean: Two-Sample Tests for High-Dimensional Mean Vectors

## Description

Calculates p-value of the test for testing equality of two-sample high-dimensional mean vectors proposed by Bai and Saranadasa (1996) based on permutation.

## Usage

 `1` ```epval_Bai1996(sam1, sam2, n.iter = 1000, seeds) ```

## Arguments

 `sam1` an n1 by p matrix from sample population 1. Each row represents a p-dimensional sample. `sam2` an n2 by p matrix from sample population 2. Each row represents a p-dimensional sample. `n.iter` a numeric integer indicating the number of permutation iterations. The default is 1,000. `seeds` a vector of seeds for each permutation or parametric bootstrap resampling iteration; this is optional.

## Details

See the details in `apval_Bai1996`.

## Value

A list including the following elements:

 `sam.info` the basic information about the two groups of samples, including the samples sizes and dimension. `cov.assumption` this output reminds users that the two sample populations have a common covariance matrix. `method` this output reminds users that the p-values are obtained using permutation. `pval` the p-value of the test proposed by Bai and Saranadasa (1996).

## Note

The permutation technique assumes that the distributions of the two sample populations are the same under the null hypothesis.

## References

Bai ZD and Saranadasa H (1996). "Effect of high dimension: by an example of a two sample problem." Statistica Sinica, 6(2), 311–329.

`apval_Bai1996`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```#library(MASS) #set.seed(1234) #n1 <- n2 <- 50 #p <- 200 #mu1 <- rep(0, p) #mu2 <- mu1 #mu2[1:10] <- 0.2 #true.cov <- 0.4^(abs(outer(1:p, 1:p, "-"))) # AR1 covariance #sam1 <- mvrnorm(n = n1, mu = mu1, Sigma = true.cov) #sam2 <- mvrnorm(n = n2, mu = mu2, Sigma = true.cov) # increase n.iter to reduce Monte Carlo error. #epval_Bai1996(sam1, sam2, n.iter = 10) ```