EEL_est: Extended empirical log likelihood ratio for parameters...
In eel: Extended Empirical Likelihood

Description Usage Arguments Value Author(s) See Also Examples

Calculate the extended empirical log likelihood ratio for parameters defined by estimating equations

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EEL_est(x, theta, theta_tilda, equation)
## Default S3 method:
EEL_est(x, theta, theta_tilda, equation)

`x`	Data matrix.
`theta`	Value at which the EEL for the parameters defined by estimating equations will be evaluated.
`theta_tilda`	The maximum empirical likelihood estimator of the unknown parameter.
`equation`	The estimating equation, must be put inside quotation marks and has to be a function of theta.

An object of class EEL, basically a list including elements

`theta`	value at which the EEL for the parameters defined by estimating equations will be evaluated;
`prime`	the prime-image inside the convex hull for the point theta;
`estimating equation`	the estimating equation;
`expansion`	the value of the expansion factor gamma;
`oel_log`	the original empirical log likelihood ratio value;
`eel_log`	the extended empirical log likelihood ratio value.

Yu Zhang

EMLogLR,exp_factor_est,prime_image_est,print.EEL,summary.EEL,eel-package, EEL

# 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(5,3), use
theta_tilda=colMeans(multnorm-as.vector(c(5,3)))
EEL_est(x=multnorm,theta=c(5,3),theta_tilda, "x-theta")