SD2008.TS.NABT {HDNRA} | R Documentation |
Normal-approximation-based test for two-sample problem proposed by Srivastava and Du (2008)
Description
Srivastava and Du (2008)'s test for testing equality of two-sample high-dimensional mean vectors with assuming that two covariance matrices are the same.
Usage
SD2008.TS.NABT(y1, y2)
Arguments
y1 |
The data matrix ( |
y2 |
The data matrix ( |
Details
Suppose we have two independent high-dimensional samples:
\boldsymbol{y}_{i1},\ldots,\boldsymbol{y}_{in_i}, \;\operatorname{are \; i.i.d. \; with}\; \operatorname{E}(\boldsymbol{y}_{i1})=\boldsymbol{\mu}_i,\; \operatorname{Cov}(\boldsymbol{y}_{i1})=\boldsymbol{\Sigma},i=1,2.
The primary object is to test
H_{0}: \boldsymbol{\mu}_1 = \boldsymbol{\mu}_2\; \operatorname{versus}\; H_{1}: \boldsymbol{\mu}_1 \neq \boldsymbol{\mu}_2.
Srivastava and Du (2008) proposed the following test statistic:
T_{SD} = \frac{n^{-1}n_1n_2(\bar{\boldsymbol{y}}_1 - \bar{\boldsymbol{y}}_2)^\top \boldsymbol{D}_S^{-1}(\bar{\boldsymbol{y}}_1 - \bar{\boldsymbol{y}}_2) - \frac{(n-2)p}{n-4}}{\sqrt{2 \left[\operatorname{tr}(\boldsymbol{R}^2) - \frac{p^2}{n-2}\right] c_{p, n}}},
where \bar{\boldsymbol{y}}_{i},i=1,2
are the sample mean vectors, \boldsymbol{D}_S
is the diagonal matrix of sample variance, \boldsymbol{R}
is the sample correlation matrix and c_{p, n}
is the adjustment coefficient proposed by Srivastava and Du (2008).
They showed that under the null hypothesis, T_{SD}
is asymptotically normally distributed.
Value
A list of class "NRtest"
containing the results of the hypothesis test. See the help file for NRtest.object
for details.
References
Srivastava MS, Du M (2008). “A test for the mean vector with fewer observations than the dimension.” Journal of Multivariate Analysis, 99(3), 386–402. doi:10.1016/j.jmva.2006.11.002.
Examples
library("HDNRA")
data("COVID19")
dim(COVID19)
group1 <- as.matrix(COVID19[c(2:19, 82:87), ]) ## healthy group
group2 <- as.matrix(COVID19[-c(1:19, 82:87), ]) ## COVID-19 patients
SD2008.TS.NABT(group1,group2)