shrinkTEGS: Default shrinkage estimation of covariance matrices

Description

The function adds a small quantity to the diagonals of covariance matrix estimates to regularize them.

Usage

shrinkTEGS(s, s1, s2, param = list(probs = 0.05, type = "min"))

Arguments

covariance matrix estimte in the pooled sample

sample covariance matrix estimate in class 1

sample covariance matrix estimate in class 2

param

list of parameters:

type: minimum (min), maximum (max) or optimal (opt)
probs: the numeric value of probability with value in [0,1]

Details

To determine the quantity to add to the diagonals of covariance matrices, the function:

finds the distributions of the sample variances of the p variables in the two classes and in the pooled sample
computes the probs percentile of each of these distributions
use the minimum, maximum or optimal (one for each matrix) (type)

References

Huang, Y.-T. and Lin, X. (2013). Gene set analysis using variance component tests. BMC Bioinformatics, 14(1), 210.

Examples

Run this code

# NOT RUN {
if(require(mvtnorm)){

  ## Generate two random samples of size 50 from two multivariate normal distributions
  # sample size
  n<-50
  # true parameters of class 1 and class 2
  param.class1<-simulation$condition1
  param.class2<-simulation$condition2$`5`$`2`
  # simulated dataset
  data.class1<-rmvnorm(n = n,mean =param.class1$mu ,sigma =param.class1$S)
  data.class2<-rmvnorm(n = n,mean =param.class2$mu ,sigma=param.class2$S)
  data<-rbind(data.class1,data.class2)
  classes<-c(rep(1,nrow(data.class1)),rep(2,nrow(data.class2)))

  ## estimated parameters: maximum likelihood estimate
  s<-cov(data)
  s1<-cov(data.class1)
  s2<-cov(data.class2)

  ## default parameters:
  # use the minimum of median variances distributions of the three supplied covariance matrices
  def.shrink<-shrinkTEGS(s,s1,s2)
  def.shrink$lambda

  ## use customize lamdas
  def.shrink<-shrinkTEGS(s,s1,s2,param = list(lambda=c(0.1,0.2,0.3)))
  def.shrink$lambda

  # use for each covariance matrix the 0.4 percentile of its variances distributions
  def.shrink<-shrinkTEGS(s,s1,s2,param = list(type="opt",probs=0.4))
  def.shrink$lambda
}
# }