findL3 {ELYP}

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.

Author(s)

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)