ts_zzz2020 {HDNRA} | R Documentation |
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.
ts_zzz2020(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.(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.
A (list) object of S3
class htest
containing the following elements:
the p-value of the test proposed by Zhang et al. (2020).
the test statistic proposed by Zhang et al. (2020).
estimated approximate degrees of freedom of Zhang et al. (2020)'s test.
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.
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_zzz2020(y1, y2)