eel-package {eel} R Documentation

## 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 of help topics:

EEL                     Extended empirical log likelihood ratio for the
mean
EEL_est                 Extended empirical log likelihood ratio for
parameters defined by estimating equaitons
EMLogLR                 Original empirical log likelihood ratio
eel-package             Extended Empirical Likelihood
exp_factor              Calculating expansion factor for EEL for the
mean
exp_factor_est          Calculating expansion factor for EEL for
parameters defined by estimating equations
prime_image             Calculating prime-image based on similarity
mapping for the mean
prime_image_est         Calculating prime-image based on similarity
mapping for parameters defined by estimating
equations
print.EEL               Printing EEL objects
summary.EEL             Summarizing EEL objects


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 <yuz@uvic.ca>

### 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

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)


[Package eel version 1.1 Index]