ELYP (version 0.7-1)

findL3: 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 ...

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.

Value

• A list with the following components:
• Lower
  the lower confidence bound.
• minParameterNloglik
  Final values of the 4 parameters, and the log likelihood.

Details

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).

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 0.5 min to run.
# findL3(NPmle=c(1.816674, -1.002082), ConfInt=c(1.2, 0.5, 10),   
#           LogLikfn=myLLfun, Pfun=Pfun, dataMat=GastricCancer)