ZZZ2020.TS.2cNRT {HDNRA} | R Documentation |
Normal-reference-test with two-cumulant (2-c) matched $\chi^2$-approximation for two-sample problem proposed by Zhang et al. (2020)
Description
Zhang et al. (2020)'s test for testing equality of two-sample high-dimensional mean vectors with assuming that two covariance matrices are the same.
Usage
ZZZ2020.TS.2cNRT(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.
Zhang et al.(2020) proposed the following test statistic:
T_{ZZZ} = \frac{n_1n_2}{np}(\bar{\boldsymbol{y}}_1 - \bar{\boldsymbol{y}}_2)^\top \hat{\boldsymbol{D}}^{-1}(\bar{\boldsymbol{y}}_1 - \bar{\boldsymbol{y}}_2),
where \bar{\boldsymbol{y}}_{i},i=1,2
are the sample mean vectors, \hat{\boldsymbol{D}}
is the diagonal matrix of sample covariance matrix.
They showed that under the null hypothesis, T_{ZZZ}
and a chi-squared-type mixture have the same limiting distribution.
Value
A list of class "NRtest"
containing the results of the hypothesis test. See the help file for NRtest.object
for details.
References
Zhang L, Zhu T, Zhang J (2020). “A simple scale-invariant two-sample test for high-dimensional data.” Econometrics and Statistics, 14, 131–144. doi:10.1016/j.ecosta.2019.12.002.
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
ZZZ2020.TS.2cNRT(group1,group2)