EEL_est {eel} R Documentation

## 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)
## Default S3 method:
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.

### Author(s)

Yu Zhang

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")



[Package eel version 1.1 Index]