ELYP (version 0.7-1)

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 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 ...

Pfun

A function of 2 variables: NPmle[1]+NPmle[2]. Must be able to take 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 upper confidence bound.
• 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

## 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)