ts_zz2022 {HDNRA} | R Documentation |
Zhang and Zhu (2022)'s test for testing equality of two-sample high-dimensional mean vectors with assuming that two covariance matrices are the same.
ts_zz2022(y1, y2)
y1 |
The data matrix ( |
y2 |
The data matrix ( |
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.(2022) proposed the following test statistic:
T_{ZZ} = \frac{n_1n_2}{n} \|\bar{\boldsymbol{y}}_1 - \bar{\boldsymbol{y}}_2\|^2-\operatorname{tr}(\hat{\boldsymbol{\Sigma}}),
where \bar{\boldsymbol{y}}_{i},i=1,2
are the sample mean vectors and \hat{\boldsymbol{\Sigma}}
is the pooled sample covariance matrix.
They showed that under the null hypothesis, T_{ZZ}
and a chi-squared-type mixture have the same normal or non-normal limiting distribution.
A (list) object of S3
class htest
containing the following elements:
the p-value of the test proposed by Zhang and Zhu (2022).
the test statistic proposed by Zhang and Zhu (2022).
parameter used in Zhang and Zhu (2022)'s test
parameter used in Zhang and Zhu (2022)'s test
estimated approximate degrees of freedom of Zhang and Zhu (2022)'s test.
Zhang J, Zhu T (2022). “A revisit to Bai–Saranadasa's two-sample test.” Journal of Nonparametric Statistics, 34(1), 58–76. doi:10.1080/10485252.2021.2015768.
set.seed(1234)
n1 <- 20
n2 <- 30
p <- 50
mu1 <- t(t(rep(0, p)))
mu2 <- mu1
rho <- 0.1
y <- (-2 * sqrt(1 - rho) + sqrt(4 * (1 - rho) + 4 * p * rho)) / (2 * p)
x <- y + sqrt((1 - rho))
Gamma <- matrix(rep(y, p * p), nrow = p)
diag(Gamma) <- rep(x, p)
Z1 <- matrix(rnorm(n1 * p, mean = 0, sd = 1), p, n1)
Z2 <- matrix(rnorm(n2 * p, mean = 0, sd = 1), p, n2)
y1 <- Gamma %*% Z1 + mu1 %*% (rep(1, n1))
y2 <- Gamma %*% Z2 + mu2 %*% (rep(1, n2))
ts_zz2022(y1, y2)