eel (version 1.1)

EEL_est: Extended empirical log likelihood ratio for parameters defined by estimating equaitons

Description

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

Usage

EEL_est(x, theta, theta_tilda, equation)
"EEL_est"(x, theta, theta_tilda, equation)

Arguments

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.

Value

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.

See Also

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

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