ELYP (version 0.7-3)

findL2d: Find the Wilks Confidence Interval Lower Bound from the Given 2-d Empirical Likelihood Ratio Function

Description

This function is a sister function to findU2d( ). It uses simple search algorithm to find the lower 95% Wilks confidence limits based on the log likelihood function supplied. The likelihood have two parameters: beta1, beta2 and the the confidence interval is for a 1-d parameter defined by Pfun(beta1, beta2).

Usage

findL2d(NPmle, ConfInt, LogLikfn, Pfun, dataMat, level=3.84)

Arguments

NPmle

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

ConfInt

a vector of length 2. These are APPROXIMATE length of confidence intervals, as initial guess.

LogLikfn

a function that takes input of beta=(beta1, beta2) and dataMat, and output the log likelihood value.

Pfun

A function of 2 variables: beta1 and beta2. Must be able to take a vector input. Example: Pfun(x1, x2)= x1.

dataMat

a matrix of data. for the function LogLikfn.

level

Confidence level. Default to 3.84 (95 percent).

Value

A list with the following components:

Lower

the lower confidence bound for Pfun.

minParameterNloglik

Final values of the 2 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

# NOT RUN {
## example with tied observations
x <- c(1, 1.5, 2, 3, 4, 5, 6, 5, 4, 1, 2, 4.5)
d <- c(1,   1, 0, 1, 0, 1, 1, 1, 1, 0, 0,   1)
# }