| 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. |
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)