ZZ2022.TSBF.3cNRT {HDNRA} | R Documentation |
Normal-reference-test with three-cumulant (3-c) matched $\chi^2$-approximation for two-sample BF problem proposed by Zhang and Zhu (2022)
Description
Zhang and Zhu (2022)'s test for testing equality of two-sample high-dimensional mean vectors without assuming that two covariance matrices are the same.
Usage
ZZ2022.TSBF.3cNRT(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,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 and Zhu (2022) proposed the following test statistic:
T_{ZZ} = \|\bar{\boldsymbol{y}}_1 - \bar{\boldsymbol{y}}_2\|^2-\operatorname{tr}(\hat{\boldsymbol{\Omega}}_n),
where \bar{\boldsymbol{y}}_{i},i=1,2
are the sample mean vectors and \hat{\boldsymbol{\Omega}}_n
is the estimator of \operatorname{Cov}(\bar{\boldsymbol{y}}_1-\bar{\boldsymbol{y}}_2)
.
They showed that under the null hypothesis, T_{ZZ}
and a chi-squared-type mixture have the same normal or non-normal 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 J, Zhu T (2022). “A further study on Chen-Qin’s test for two-sample Behrens–Fisher problems for high-dimensional data.” Journal of Statistical Theory and Practice, 16(1), 1. doi:10.1007/s42519-021-00232-w.
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
ZZ2022.TSBF.3cNRT(group1, group2)