eel-package: Extended Empirical Likelihood

In eel: Extended Empirical Likelihood

Description

Compute the extended empirical log likelihood ratio (Tsao & Wu, 2014) for the mean and parameters defined by estimating equations.

Details

Index: This package was not yet installed at build time.
The extended empirical log likelihood ratio for the mean is computed by calling the function EEL(), and that for the parameter defined estimating equations is computed by calling the function EEL_est(). This package requires pre-installation of two packages "emplik" and "rootSolve". These are needed for computing the prime image of a point theta as well as the final extended empirical log likelihood ratio value as described in Tsao and Wu (2013, 2014). Only the first-order EEL discussed Tsao and Wu (2013, 2014) is included in this package.

Author(s)

Fan Wu and Yu Zhang

Maintainer: Yu Zhang <[e-mail]>

References

Tsao, M. (2013). Extending the empirical likelihood by domain expansion. The Canadian Journal of Statistics, 41 (2), 257-274.

Tsao, M., & Wu, F. (2013). Empirical likelihood on the full parameter space. Annals of Statistics, 0 (00), 1-21. doi: 10.1214/13-AOS1143

Tsao, M., & Wu, F. (2014). Extended empirical likelihood for estimating equations.Biometrika, 1-8. doi: 10.1093/biomet/asu014

See Also

EMLogLR, EEL, EEL_est, exp_factor, prime_image, prime_image_est, exp_factor_est,

Examples

# EXAMPLE: computing the EEL for the mean of a bivariate random variable
# Generating a sample of n=40 bivariate observations. 
# For this example, we do this through a univariate normal random number generator.

uninorm<- rnorm(40*2,5,1)                          
multnorm<-matrix(uninorm,ncol=2)

# To calculate the EEL for a point theta=c(5,2), use
EEL(x=multnorm,theta=c(5,2))

# an example to use the EEL_est in the case of estimating equation

# generate regression dataset
# random variable x
dmx2<-runif(100,min=0,max=100)
dmx<-matrix(0,100,2)
dmx[,1]=1
dmx[,2]=dmx2

# set the initial beta value
beta0<-c(1,2)  

# generate random errors and calculate the response variable
errdata<-rnorm(100,0,1)
ydata<-dmx%*%beta0+errdata 

# calculate the maximum empirical likelihood estimates
beta_lse<-solve(t(dmx)%*%dmx)%*%(t(dmx)%*%ydata)

num=EEL_est(x=dmx,theta=c(1,2),theta_tilda=beta_lse,
"gx<-matrix(0,nrow=100,ncol=2) 
for(i in 1:2){gx[,i]<-dmx[,i]*(ydata-dmx%*%as.matrix(theta))} 
gx")
summary(num)

Example output

Loading required package: emplik
Loading required package: quantreg
Loading required package: SparseM

Attaching package: 'SparseM'

The following object is masked from 'package:base':

    backsolve

Loading required package: rootSolve
Call:
EEL.default(x = multnorm, theta = c(5, 2))

 log eel ratio: 
[1] 100.3003
Call:
EEL_est.default(x = dmx, theta = c(1, 2), theta_tilda = beta_lse, 
    equation = "gx<-matrix(0,nrow=100,ncol=2) \\nfor(i in 1:2){gx[,i]<-dmx[,i]*(ydata-dmx%*%as.matrix(theta))} \\ngx")

 theta: 
     [,1]
[1,]    1
[2,]    2

 estimating equation: 
[1] "gx<-matrix(0,nrow=100,ncol=2) \nfor(i in 1:2){gx[,i]<-dmx[,i]*(ydata-dmx%*%as.matrix(theta))} \ngx"

 log oel ratio: 
[1] 652.192

 prime image: 
          [,1]
[1,] 0.9996748
[2,] 2.0000217

 expasion factor: 
[1] 1.00761

 log eel ratio: 
[1] 4297.513

eel documentation built on May 2, 2019, 5:11 a.m.