findL3 {ELYP} R Documentation

## Find the Wilks Confidence Interval Lower Bound from the Given Empirical Likelihood Ratio Function

### Description

This program is the sister program to the findU3( ). It uses simple search to find the lower 95% Wilks confidence limits based on the log likelihood function supplied.

### Usage

findL3(NPmle, ConfInt, LogLikfn, Pfun, level=3.84, dataMat)


### Arguments

 NPmle a vector containing the two NPMLE: beta1 hat and beta2 hat. ConfInt a vector of length 3. LogLikfn a function that compute the loglikelihood. Typically this has three parameters: beta1, beta2 and lam, in a Yang-Prentice model context. Pfun a function that takes the input of 3 parameter values (beta1,beta2 and Mulam) and returns a parameter that we wish to find the confidence Interval of (here only the Lower Value). level confidence level. Default to 3.84 for 95 percent. dataMat a matrix.

### Details

The empirical likelihood for Y-P model has parameters: beta1, beta2 and a baseline. The baseline is converted to a 1-d parameter feature via Hfun, and then amount controled by lam.

Basically we repeatedly testing the value of the parameter, until we find those which the -2 log likelihood value is equal to 3.84 (or other level, if set differently).

### Value

A list with the following components:

 Lower the lower confidence bound. minParameterNloglik Final values of the 4 parameters, and the log likelihood.

Mai Zhou

### References

Zhou, M. (2002). Computing censored empirical likelihood ratio by EM algorithm. JCGS

### Examples

## Here Mulam is the value of int g(t) d H(t) = Mulam
## For example g(t) = I[ t <= 2.0 ]; look inside myLLfun().

Pfun <- function(b1, b2, Mulam) {
alpha <- exp(-Mulam)
TrtCon <- 1/(alpha*exp(-b1) + (1-alpha)*exp(-b2))
return(TrtCon)
}

data(GastricCancer)

# The following will take about 10 sec. to run on i7 CPU.
# findL3(NPmle=c(1.816674, -1.002082), ConfInt=c(1.2, 0.5, 10),
#           LogLikfn=myLLfun, Pfun=Pfun, dataMat=GastricCancer)



[Package ELYP version 0.7-5 Index]