findU2d: Find the Wilks Confidence Interval Upper Bound from the Given...

In ELYP: Empirical Likelihood Analysis for the Cox Model and Yang-Prentice (2005) Model

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.

Author(s)

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)

ELYP documentation built on May 2, 2019, 5:17 a.m.