findU2d {ELYP} R Documentation

## 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)


### 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).

### 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.

### 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.

Mai Zhou

### 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)


[Package ELYP version 0.7-5 Index]