ELYP (version 0.7-5)

findU2d: Find the Wilks Confidence Interval Upper Bound from the Given 2-d Empirical Likelihood Ratio Function

Description

This program uses simple search algorithm to find the upper 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 =Pfun(beta1,beta2).

Usage

findU2d(NPmle, ConfInt, LogLikfn, Pfun, dataMat, level=3.84)

Value

A list with the following components:

Upper

the upper confidence bound for Pfun.

maxParameterNloglik

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 the input of beta and dataMat and output the logliklihood value.

Pfun

A function of 2 variables: beta1 and beta2. Must be able to take vector input. output one value: The statistic you try to find the confidence interval of. 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).

This problem may also be solved by the nuisance parameter/profiling technique.

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)