ZZ2022.TS.3cNRT: Normal-reference-test with three-cumulant (3-c) matched...

In HDNRA: High-Dimensional Location Testing with Normal-Reference Approaches

Normal-reference-test with three-cumulant (3-c) matched $\chi^2$-approximation for two-sample problem proposed by Zhang and Zhu (2022)

Description

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.

Usage

ZZ2022.TS.3cNRT(y1, y2)

Arguments

y1	The data matrix (n_1 \times p) from the first population. Each row represents a p-dimensional observation.
y2	The data matrix (n_2 \times p) from the second population. Each row represents a p-dimensional observation.

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.(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.

Value

A list of class "NRtest" containing the results of the hypothesis test. See the help file for NRtest.object for details.

References

\insertRef

zhang2022revisitHDNRA

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.TS.3cNRT(group1, group2)

HDNRA documentation built on Oct. 30, 2024, 9:28 a.m.