get.beta {icmm}

Obtain model coefficient without assuming prior on structure of predictors.

Description

Given a sufficient statistic for a regression coefficient, this funciton estimates a regression coefficient without assuming prior on structure of predictors.

Usage

get.beta(SS, w, alpha, scaledfactor)

Arguments

SS

a scalar value of sufficient statistic for a regression coefficient.

w

a scalar value of mixing weight.

alpha

a scalar value of hyperparameter alpha.

scaledfactor

a scalar value of multiplicative factor.

Details

Empirical Bayes thresholding is employed to obtain a posterior median of a regression coefficient.

Value

a scalar value of regression coefficient.

Author(s)

Vitara Pungpapong, Min Zhang, Dabao Zhang

Examples

data(simGaussian)
Y<-as.matrix(simGaussian[,1])
X<-as.matrix(simGaussian[,-1])
n<-dim(X)[1]
# Obtain initial values from lasso
data(initbetaGaussian)
beta<-as.matrix(initbetaGaussian)
# Initiate all other parameters
w<-0.5
alpha<-0.5
sigma<-get.sigma(Y=Y, X=X, beta=beta, alpha=alpha)
# Obtain a sufficient statistic
j<-1
Yres<-Y-X%*%beta+X[,j]*beta[j,1]
sxy<-t(Yres)%*%X[,j]
ssx<-sum(X[,j]^2)
SS<-sqrt(n-1)*sxy/(sigma*ssx)
beta[j,1]<-get.beta(SS=SS, w=w, alpha=alpha, scaledfactor=sigma/sqrt(n-1))