findU3 {ELYP}

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

Description

This program uses simple search to find the upper 95% Wilks confidence limits based on the log likelihood function supplied.

Usage

findU3(NPmle, ConfInt, LogLikfn, Pfun, level=3.84, dataMat)

Arguments

NPmle

a vector containing the two NPMLEs: beta1 hat and beta2 hat.

ConfInt

a vector of length 3. Approximate length of the 3 confidence intervals: beta1, beta2 and lambda. They are used as initial search steps.

LogLikfn

a function that takes input of beta1, beta2 lam, dataMat, and output the log likelihood value.

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 Upper Value.

level

confidence level, default to 3.84 for 95 percent.

dataMat

a matrix. for the loglik computation.

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).

Value

A list with the following components:

Upper

the upper confidence bound.

maxParameterNloglik

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(). 

data(GastricCancer)

# The following will take about 10 sec. to run on an i7-4690 CPU.
# findU3(NPmle=c(1.816674, -1.002082), ConfInt=c(1.2, 0.5, 10),   
#          LogLikfn=myLLfun, Pfun=Pfun, dataMat=GastricCancer)