Package 'Docovt'

Title: Distributed Online Covariance Matrix Tests
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>.
Authors: Guangbao Guo [aut, cre] (ORCID: <https://orcid.org/0000-0002-4115-6218>), Congfan Zhang [aut]
Maintainer: Guangbao Guo <[email protected]>
License: MIT + file LICENSE
Version: 0.3
Built: 2026-05-31 08:46:05 UTC
Source: https://github.com/cran/Docovt

Help Index

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:

H0:Σ1=Σ2H_0 : \Sigma_1 = \Sigma_2

Σ1\Sigma_1 and Σ2\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)

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

Description

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

H0:Σn=Σ0H_0 : \Sigma_n = \Sigma_0

where Σn\Sigma_n is the covariance of data model and Σ0\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×p)(n\times p) data matrix where each row is an observation.
Sigma0

a (p×p)(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

H0:Σ1=Σ2H_0 : \Sigma_1 = \Sigma_2

where Σ1\Sigma_1 and Σ2\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×p)(m\times p) matrix where each row is an observation from the first dataset.
Y

an (n×p)(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)

corneal

Description

This dataset was acquired during a keratoconus study, a collaborative project involving Ms.Nancy Tripoli and Dr.Kenneth L.Cohen of Department of Ophthalmology at the University of North Carolina, Chapel Hill. The fitted feature vectors for the complete corneal surface dataset collectively into a feature matrix with dimensions of 150 × 2000.

Usage

data(corneal)

Format

'corneal'

A data frame with 150 observations on the following 4 groups.

normal group1

row 1 to row 43 in total 43 rows of the feature matrix correspond to observations from the normal group

unilateral suspect group2

row 44 to row 57 in total 14 rows of the feature matrix correspond to observations from the unilateral suspect group

suspect map group3

row 58 to row 78 in total 21 of the feature matrix correspond to observations from the suspect map group

clinical keratoconus group4

row 79 to row 150 in total 72 of the feature matrix correspond to observations from the clinical keratoconus group

Examples

data(corneal)
dim(corneal)
group1 <- as.matrix(corneal[1:43, ]) ## normal group
dim(group1)
group2 <- as.matrix(corneal[44:57, ]) ## unilateral suspect group
dim(group2)
group3 <- as.matrix(corneal[58:78, ]) ## suspect map group
dim(group3)
group4 <- as.matrix(corneal[79:150, ]) ## clinical keratoconus group
dim(group4)

COVID19

Description

A COVID19 data set from NCBI with ID GSE152641. The data set profiled peripheral blood from 24 healthy controls and 62 prospectively enrolled patients with community-acquired lower respiratory tract infection by SARS-COV-2 within the first 24 hours of hospital admission using RNA sequencing.

Usage

data(COVID19)

Format

'COVID19'

A data frame with 86 observations on the following 2 groups.

healthy group1

row 2 to row 19, and row 82 to 87, in total 24 healthy controls

patients group2

row 20 to 81, in total 62 prospectively enrolled patients

Examples

data(COVID19)
dim(COVID19)
group1 <- as.matrix(COVID19[c(2:19, 82:87), ]) ## healthy group
dim(group1)
group2 <- as.matrix(COVID19[-c(1:19, 82:87), ]) ## COVID-19 patients
dim(group2)

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:

H0:Σ1=Σ2H_0 : \Sigma_1 = \Sigma_2

Σ1\Sigma_1 and Σ2\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)

miRNA

Description

A three factor level variable corresponding to cancer type

Usage

data(miRNA)

Format

Dataframe with 21 samples and 537 variables

columns

variables

rows

samples

Examples

data(miRNA)

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:

H0:Σ1=Σ2H_0 : \Sigma_1 = \Sigma_2

Σ1\Sigma_1 and Σ2\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:

H0:Σ1=Σ2H_0 : \Sigma_1 = \Sigma_2

Σ1\Sigma_1 and Σ2\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:

H0:Σ1=Σ2H_0 : \Sigma_1 = \Sigma_2

Σ1\Sigma_1 and Σ2\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 Srivastava, Yanagihara, and Kubokawa (2014)

Description

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

H0:Σn=Σ0H_0 : \Sigma_n = \Sigma_0

where Σn\Sigma_n is the covariance of data model and Σ0\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×p)(n\times p) data matrix where each row is an observation.
Sigma0

a (p×p)(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)