Title: Distributed Online Covariance Matrix Tests
Date: 2025-06-29
Version: 0.2
Description: Distributed Online Covariance Matrix Tests 'Docovt' is a powerful tool designed to efficiently process and analyze distributed datasets. It enables users to perform covariance matrix tests in an online, distributed manner, making it highly suitable for large-scale data analysis. By leveraging advanced computational techniques, 'Docovt' ensures robust and scalable solutions for statistical analysis, particularly in scenarios where data is dispersed across multiple nodes or sources. This package is ideal for researchers and practitioners working with high-dimensional data, providing a flexible and efficient framework for covariance matrix estimation and hypothesis testing. The philosophy of 'Docovt' is described in Guo G.(2025) <doi:10.1016/j.physa.2024.130308>.
License: MIT + file LICENSE
Encoding: UTF-8
RoxygenNote: 7.3.2
Imports: stats
Suggests: testthat (≥ 3.0.0)
Config/testthat/edition: 3
NeedsCompilation: no
Packaged: 2025-06-29 08:52:54 UTC; lenovo
Author: Guangbao Guo ORCID iD [aut, cre], Congfan Zhang [aut]
Maintainer: Guangbao Guo <ggb11111111@163.com>
Depends: R (≥ 3.5.0)
Repository: CRAN
Date/Publication: 2025-06-30 02:10:02 UTC

Two-Sample Covariance Test by Cai, Liu and Xia (2013)

Description

Given two sets of data matrices X and Y, where X is an n1 rows and p cols matrix and Y is an n2 rows and p cols matrix, we conduct hypothesis testing of the covariance matrix between two samples. The null hypothesis is:

H_0 : \Sigma_1 = \Sigma_2

\Sigma_1 and \Sigma_2 are the sample covariance matrices of X and Y respectively. This test method is based on the test method proposed by Cai, Liu and Xia (2013). When the pval value is less than the significance coefficient (generally 0.05), the null hypothesis is rejected.

Usage

CLX(X,Y)

Arguments

X

A matrix of n1 by p

Y

A matrix of n2 by p

Value

stat

a test statistic value.

pval

a test p_value.

References

Cai, T. T., Liu, W., and Xia, Y. (2013). Two-sample covariance matrix testing and support recovery in high-dimensional and sparse settings. Journal of the American Statistical Association, 108(501):265-277.

Examples

## generate X and Y.
p= 500;  n1 = 100; n2 = 150
X=matrix(rnorm(n1*p), ncol=p)
Y=matrix(rnorm(n2*p), ncol=p)
## run test
CLX(X,Y)

Two-Sample Covariance Test by Li and Chen (2012)

Description

Given two sets of data matrices X and Y, where X is an n1 rows and p cols matrix and Y is an n2 rows and p cols matrix, we conduct hypothesis testing of the covariance matrix between two samples. The null hypothesis is:

H_0 : \Sigma_1 = \Sigma_2

\Sigma_1 and \Sigma_2 are the sample covariance matrices of X and Y respectively. This test method is based on the test method proposed by Li and Chen (2012). When the pval value is less than the significance coefficient (generally 0.05), the null hypothesis is rejected.

Usage

LC(X,Y)

Arguments

X

A matrix of n1 by p

Y

A matrix of n2 by p

Value

stat

a test statistic value.

pval

a test p_value.

References

Li, J. and Chen, S. X. (2012). Two sample tests for high-dimensional covariance matrices. The Annals of Statistics, 40(2):908-940.

Examples

## generate X and Y.
p= 500;  n1 = 100; n2 = 150
X=matrix(rnorm(n1*p), ncol=p)
Y=matrix(rnorm(n2*p), ncol=p)
## run test
LC(X,Y)

Two-Sample Covariance Test by Yu, Li and Xue (2022)

Description

Given two sets of data matrices X and Y, where X is an n1 rows and p cols matrix and Y is an n2 rows and p cols matrix,, we conduct hypothesis testing of the covariance matrix between two samples. The null hypothesis is:

H_0 : \Sigma_1 = \Sigma_2

\Sigma_1 and \Sigma_2 are the sample covariance matrices of X and Y respectively. This test method is based on the test method proposed by Yu, Li and Xue (2022). When the pval value is less than the significance coefficient (generally 0.05), the null hypothesis is rejected.

Usage

PEC(X,Y)

Arguments

X

A matrix of n1 by p

Y

A matrix of n2 by p

Value

stat

a test statistic value.

pval

a test p_value.

References

Yu, X., Li, D., and Xue, L. (2022). Fisher's combined probability test for high-dimensional covariance matrices. Journal of the American Statistical Association, (in press):1-14.

Examples

## generate X and Y.
p= 500;  n1 = 100; n2 = 150
X=matrix(rnorm(n1*p), ncol=p)
Y=matrix(rnorm(n2*p), ncol=p)
## run test
PEC(X,Y)

Two-Sample Covariance Test by Yu, Li, Xue and Li(2022)

Description

Given two sets of data matrices X and Y, where X is an n1 rows and p cols matrix and Y is an n2 rows and p cols matrix, we conduct hypothesis testing of the covariance matrix between two samples. The null hypothesis is:

H_0 : \Sigma_1 = \Sigma_2

\Sigma_1 and \Sigma_2 are the sample covariance matrices of X and Y respectively. This test method is based on the test method proposed by Yu, Li, Xue and Li (2022). When the pval value is less than the significance coefficient (generally 0.05), the null hypothesis is rejected.

Usage

PECO(X,Y,delta = NULL)

Arguments

X

A matrix of n1 by p

Y

A matrix of n2 by p

delta

A scalar used as the threshold for building PE components, usually the default value.

Value

stat

a test statistic value.

pval

a test p_value.

References

Yu, X., Li, D., Xue, L., and Li, R. (2022). Power-enhanced simultaneous test of high-dimensional mean vectors and covariance matrices with application to gene-set testing. Journal of the American Statistical Association, (in press):1-14.

Examples

## generate X and Y.
p= 500;  n1 = 100; n2 = 150
X=matrix(rnorm(n1*p), ncol=p)
Y=matrix(rnorm(n2*p), ncol=p)
## run test
PECO(X,Y)

Two-Sample Covariance Test by Yu, Li and Xue (2022)

Description

Given two sets of data matrices X and Y, where X is an n1 rows and p cols matrix and Y is an n2 rows and p cols matrix,, we conduct hypothesis testing of the covariance matrix between two samples. The null hypothesis is:

H_0 : \Sigma_1 = \Sigma_2

\Sigma_1 and \Sigma_2 are the sample covariance matrices of X and Y respectively. This test method is based on the test method proposed by Yu, Li and Xue (2022). When the pval value is less than the significance coefficient (generally 0.05), the null hypothesis is rejected.

Usage

PEF(X,Y)

Arguments

X

A matrix of n1 by p

Y

A matrix of n2 by p

Value

stat

a test statistic value.

pval

a test p_value.

References

Yu, X., Li, D., and Xue, L. (2022). Fisher's combined probability test for high-dimensional covariance matrices. Journal of the American Statistical Association, (in press):1-14.

Examples

## generate X and Y.
p= 500;  n1 = 100; n2 = 150
X=matrix(rnorm(n1*p), ncol=p)
Y=matrix(rnorm(n2*p), ncol=p)
## run test
PEF(X,Y)

One-Sample Covariance Test by Cai and Ma (2013)

Description

Given data, it performs 1-sample test for Covariance where the null hypothesis is

H_0 : \Sigma_n = \Sigma_0

where \Sigma_n is the covariance of data model and \Sigma_0 is a hypothesized covariance based on a procedure proposed by Cai and Ma (2013).

Usage

cm13(X,Sigma0, alpha)

Arguments

X

an (n\times p) data matrix where each row is an observation.

Sigma0

a (p\times p) given covariance matrix.

alpha

level of significance.

Value

a named list containing:

statistic

a test statistic value.

threshold

rejection criterion to be compared against test statistic.

reject

a logical; TRUE to reject null hypothesis, FALSE otherwise.

Examples

## generate data from multivariate normal with trivial covariance.
p = 5;n=10
X=data = matrix(rnorm(n*p), ncol=p)
alpha=0.05
Sigma0=diag(ncol(X))
cm13(X,Sigma0, alpha)

Two-Sample Covariance Test by Cai and Ma (2013)

Description

Given two sets of data, it performs 2-sample test for equality of covariance matrices where the null hypothesis is

H_0 : \Sigma_1 = \Sigma_2

where \Sigma_1 and \Sigma_2 represent true (unknown) covariance for each dataset based on a procedure proposed by Cai and Ma (2013). If statistic > threshold, it rejects null hypothesis.

Usage

cmtwo(X, Y, alpha)

Arguments

X

an (m\times p) matrix where each row is an observation from the first dataset.

Y

an (n\times p) matrix where each row is an observation from the second dataset.

alpha

level of significance.

Value

a named list containing

statistic

a test statistic value.

threshold

rejection criterion to be compared against test statistic.

reject

a logical; TRUE to reject null hypothesis, FALSE otherwise.

Examples

## generate 2 datasets from multivariate normal with identical covariance.
p= 5;  n1 = 100; n2 = 150; alpha=0.05
X=data1 = matrix(rnorm(n1*p), ncol=p)
Y=data2 = matrix(rnorm(n2*p), ncol=p)

# run test
cmtwo(X, Y, alpha)

One-Sample Covariance Test by Srivastava, Yanagihara, and Kubokawa (2014)

Description

Given data, it performs 1-sample test for Covariance where the null hypothesis is

H_0 : \Sigma_n = \Sigma_0

where \Sigma_n is the covariance of data model and \Sigma_0 is a hypothesized covariance based on a procedure proposed by Srivastava, Yanagihara, and Kubokawa (2014).

Usage

 syk(data, Sigma0, alpha)

Arguments

data

an (n\times p) data matrix where each row is an observation.

Sigma0

a (p\times p) given covariance matrix.

alpha

level of significance.

Value

a named list containing

statistic

a test statistic value.

threshold

rejection criterion to be compared against test statistic.

reject

a logical; TRUE to reject null hypothesis, FALSE otherwise.

Examples

## generate data from multivariate normal with trivial covariance.
p = 5;n=10
data = matrix(rnorm(n*p), ncol=p)
alpha=0.05
Sigma0=diag(ncol(data))
## run the test
syk(data, Sigma0, alpha)