Type: Package
Title: Collection of Robust Covariance and (Sparse) Precision Matrix Estimators
Version: 0.1
Date: 2021-07-18
Maintainer: Yunyi Shen <yshen99@wisc.edu>
Description: Collection of methods for robust covariance and (sparse) precision matrix estimation based on Loh and Tan (2018) <doi:10.1214/18-EJS1427>.
License: GPL-3
Imports: Rcpp (≥ 1.0.6), glasso, caret
LinkingTo: Rcpp, RcppArmadillo
RoxygenNote: 7.1.1
NeedsCompilation: yes
Packaged: 2021-08-03 04:02:00 UTC; yunyi
Author: Yunyi Shen ORCID iD [aut, cre], David Simcha [cph]
Repository: CRAN
Date/Publication: 2021-08-04 10:00:05 UTC

Sample contaminated normal

Description

This function samples normal distribution with normal contamination

Usage

conta_normal(
  n,
  Omega,
  byrow = FALSE,
  cont_rate = 0.05,
  mu = 10,
  sd = sqrt(0.2)
)

Arguments

n

samplesize

Omega

precision matrix of the normal

byrow

whether the contamination happened by row? FALSE stand for cellwise contamination

cont_rate

how many cells/rows are contaminated?

mu

mean of the contamination

sd

standard deviation of the contamination

Value

a matrix of contaminated (multivariate) normal distributed data, row as sample

Kendall's tau

Description

This routine calculates the Kendall's tau

Usage

corKendall(data)

Arguments

data

the n by p raw data matrix

Value

a matrix with dimension p by p, Kendall's tau

Examples

corKendall(matrix(rnorm(500),100,5))

Quadrant correlation coefficients

Description

This routine calculates Quadrant correlation coefficients

Usage

corQuadrant(data)

Arguments

data

the n by p raw data matrix

Value

a matrix with dimension p by p, Quadrant correlation coefficients

Examples

corQuadrant(matrix(rnorm(500),100,5))

Spearman correlation

Description

This routine calculates the Spearman correlation

Usage

corSpearman(data)

Arguments

data

the n by p raw data matrix

Value

a matrix with dimension p by p of spearman correlations

Examples

corSpearman(matrix(rnorm(500),100,5))

Gnanadesikan-Kettenring estimator for *covariance*

Description

This routine calculates the Gnanadesikan-Kettenring estimator, diagonal will be MAD

Usage

covGK(data)

Arguments

data

the n by p raw data matrix

Value

a matrix with dimension p by p, GK estimator, note that it's not necessarily positive

Examples

covGK(matrix(rnorm(500),100,5))

NPD estimator for *covariance* based on Qn

Description

This routine calculates the NPD estimator for *covariance* based on Qn

Usage

covNPD(data, eigenTol = 1e-06, convTol = 1e-07, psdTol = 1e-08, maxit = 1000L)

Arguments

data

the n by p raw data matrix

eigenTol

tolerance in eigen system, used in finding nearest positive matrix

convTol

tolerance in cov, used in finding nearest positive matrix

psdTol

tolerance in psd, used in finding nearest positive matrix

maxit

max iterations in finding nearest positive matrix

Value

a matrix with dimension p by p, NPD estimator

Examples

covNPD(matrix(rnorm(500),100,5))

Orthogonalized Gnanadesikan-Kettenring (OGK) estimator for *covariance*

Description

This routine calculates the Orthogonalized Gnanadesikan-Kettenring (OGK) estimator for *covariance*, using scale estimation of Gn, as in Maronna and Zamar

Usage

covOGK(data)

Arguments

data

the n by p raw data matrix

Value

a matrix with dimension p by p, OGK estimator

Examples

covOGK(matrix(rnorm(500),100,5))

SpearmanU estimator for *covariance*

Description

This routine calculates the SpearmanU, the pairwise covariance matrix estimator proposed in Oellererand Croux

Usage

covSpearmanU(data)

Arguments

data

the n by p raw data matrix

Value

a matrix with dimension p by p of spearmanU correlation

Examples

covSpearmanU(matrix(rnorm(500),100,5))

Cross validation to chose tuning parameter of glasso

Description

This routine use k fold cross validation to chose tuning parameter

Usage

cvglasso(
  data,
  k = 10,
  covest = cov,
  rhos = seq(0.1, 1, 0.1),
  evaluation = negLLrobOmega,
  ...
)

Arguments

data

The full dataset, should be a matrix or a data.frame, row as sample

k

number of folds

covest

a *function* or name of a function (string) that takes a matrix to estimate covariance

rhos

a vector of tuning parameter to be tested

evaluation

a *function* or name of a function (string) that takes only two arguments, the estimated covariance and the test covariance, when NULL, we use negative log likelihood on test sets

...

extra arguments send to glasso

Value

a matrix with k rows, each row is the evaluation loss of that fold

Examples

cvglasso(matrix(rnorm(100),20,5))

nearest positive semi-definite projection of a matrix

Description

This routine calculate the nearest positive semi0definite projection

Usage

nearPPSD(X, eigenTol = 1e-06, convTol = 1e-07, psdTol = 1e-08, maxit = 1000L)

Arguments

X

the matrix

eigenTol

tolerance in eigen system, used in finding nearest positive matrix

convTol

tolerance in cov, used in finding nearest positive matrix

psdTol

tolerance in psd, used in finding nearest positive matrix

maxit

max iterations in finding nearest positive matrix

Value

a matrix which is the nearest positive semi-definite matrix of input X

-log Likelihood on test set

Description

The default evaluation function in corss validation, -log liekihood on test set

Usage

negLLrobOmega(Sigma_hat, Sigma)

Arguments

Sigma_hat

the estimated *covariance* matrix of training set

Sigma

the *covariance* matrix of test sets

Value

-log likelihood

Alternative multivariate t distribution

Description

This routine samples alternative multivarate t distribution

Usage

raltert(n, Omega, nu)

Arguments

n

sample size

Omega

**precision** matrix of dimension p by p

nu

degree of freedom

Value

a matrix with dimension n by p, each row is a sample

Multivariate normal distribution with 0 mean

Description

This routine samples multivarate normal distribution of mean 0 from precision matrix

Usage

rmvnorm(n, Omega)

Arguments

n

sample size

Omega

**precision** matrix of dimension p by p

Value

a matrix with dimension n by p, each row is a sample

Multivariate t distribution

Description

This routine samples multivarate t distribution

Usage

rmvt(n, Omega, nu)

Arguments

n

sample size

Omega

**precision** matrix of dimension p by p

nu

degree of freedom

Value

a matrix with dimension n by p, each row is a sample

glasso with robust covariance estimations

Description

This routine fits glasso using a robust covariance matrix

Usage

robglasso(
  data,
  covest = cov,
  rho = 0.1,
  CV = FALSE,
  k = 10,
  grids = 15,
  evaluation = negLLrobOmega,
  ...
)

Arguments

data

raw data, should be a matrix or a data.frame, row as sample

covest

a *function* or name of a function (string) that takes a matrix to estimate covariance

rho

a scalar or vector of tuning parameters to be chosen, if CV=FALSE, should be a scalar, if CV=TRUE scalar input will be override and tuning parameter will be chosen based on CV

CV

bool, whether doing cross validation for tuning parameter, if set to TRUE and rho is a scalar, the candidate will be chosen automatically by log spacing between 0.01 max covariance and max covariance with number of grids

k

fold for cross validation if applicable

grids

number of candidate tuning parameters in cross validation

evaluation

a *function* or name of a function (string) that takes only two arguments, the estimated *covariance* and the test *covariace*, when NULL, we use negative log likelihood on test sets

...

extra argument sent to glasso::glasso

Value

a glasso return (see ?glasso::glasso), most important one is $X the estimated sparse precision,with an extra entry of tuning parameter lambda

Examples

robglasso(matrix(rnorm(100),20,5))