ELYP (version 0.7-5)

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)

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.

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).

Author

Mai Zhou

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

## 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)