The R package **HDNRA** includes the latest methods based on normal-reference approach to test the equality of the mean vectors of high-dimensional samples with possibly different covariance matrices. `HDNRA`

is also used to demonstrate the implementation of these tests, catering not only to the two-sample problem, but also to the general linear hypothesis testing (GLHT) problem. This package provides easy and user-friendly access to these tests. Both coded in C++ to allow for reasonable execution time using Rcpp. Besides Rcpp, the package has no strict dependencies in order to provide a stable self-contained toolbox that invites re-use.

There are two real data sets in `HDNRA`

: COVID19 and corneal.

Seven normal-reference tests for the two-sample problem: ts_zgzc2020(), ts_zz2022(), ts_zzz2020(), tsbf_zwz2023(), tsbf_zz2022(), tsbf_zzgz2021(), tsbf_zzz2023().

Five normal-reference tests for the GLHT problem in `HDNRA`

: glht_zgz2017(), glht_zz2022(), glht_zzz2022(), glhtbf_zz2022(), glhtbf_zzg2022().

Four existing tests for the two-sample problem in `HDNRA`

: ts_bs1996(), ts_sd2008(), tsbf_cq2010(), tsbf_skk2013().

Five existing tests for the GLHT problem in `HDNRA`

: glht_fhw2004(), glht_sf2006(), glht_ys2012(), glhtbf_zgz2017(), ks_s2007().

You can install and load the most recent development version of `HDNRA`

from GitHub with:

```
# Installing from GitHub requires you first install the devtools or remotes package
install.packages("devtools")
# Or
install.packages("remotes")
# install the most recent development version from GitHub
devtools::install_github("nie23wp8738/HDNRA")
# Or
remotes::install_github("nie23wp8738/HDNRA")
# load the most recent development version from GitHub
library(HDNRA)
```

Package `HDNRA`

comes with two real data sets:

```
# A COVID19 data set from NCBI with ID GSE152641.
?COVID19
# A corneal data set acquired during a keratoconus study.
?corneal
```

A simple example of how to use one of the normal-reference tests `tsbf_zwz2023`

using data set `COVID19`

:

```
data("COVID19")
group1 <- as.matrix(COVID19[c(2:19, 82:87), ]) # healthy group1
group2 <- as.matrix(COVID19[-c(1:19, 82:87), ]) # patients group2
# The data matrix for tsbf_zwz2023 should be p by n, sometimes we should transpose the data matrix
tsbf_zwz2023(t(group1), t(group2))
#>
#>
#>
#> data:
#> statistic = 4.1877, df1 = 2.7324, df2 = 171.7596, p-value = 0.008673
```

A simple example of how to use one of the normal-reference tests `glhtbf_zzg2022`

using data set `corneal`

:

```
data("corneal")
p <- dim(corneal)[2]
k <- 4
Y <- list()
group1 <- as.matrix(corneal[1:43, ]) # normal
group2 <- as.matrix(corneal[44:57, ]) # unilateral suspect
group3 <- as.matrix(corneal[58:78, ]) # suspect
group4 <- as.matrix(corneal[79:150, ]) # clinical leratoconus
Y[[1]] <- t(group1)
Y[[2]] <- t(group2)
Y[[3]] <- t(group3)
Y[[4]] <- t(group4)
dim(Y[[1]])
#> [1] 2000 43
dim(Y[[2]])
#> [1] 2000 14
dim(Y[[3]])
#> [1] 2000 21
dim(Y[[4]])
#> [1] 2000 72
n <- c(43, 14, 21, 72)
G <- cbind(diag(k - 1), rep(-1, k - 1))
glhtbf_zzg2022(Y, G, n, p)
#>
#>
#>
#> data:
#> statistic = 159.73, df = 6.1652, beta = 6.1464, p-value = 0.0002577
```

Please note that the HDNRA project is released with a Contributor Code of Conduct. By contributing to this project, you agree to abide by its terms