emplikAUC (version 0.5)

findULNEW: Finding the Upper and Lower bound of a confidence interval for theta by repeatedly testing the hypothesis for the parameter theta.

Description

This function try to find the Upper and Lower bound of a confidence interval by repeatedly testing the hypothesis for the parameter theta until we reach the given level for the "-2LLR" which is returned from the user supplied function fun.

Usage

findULNEW(step=0.01, initStep=0, fun, MLE, level=qchisq(0.95,df=1), 
           tol=.Machine$double.eps^0.5,...)

Value

It returns a list containing

Low

Lower bound of the confidence interval.

Up

Upper bound of the confidence interval.

FstepL

The error when search for Lower bound.

FstepU

The error when search for Upper bound.

Lvalue

The final likelihood ratio value for Lower bound. Should = level.

Uvalue

The final likelihood ratio value for Upper bound. Should = level.

Arguments

step

Search step. Must > 0.

initStep

The initial step from MLE. May be used if we knew the bound is far away from MLE. This help to speed up things. Should be >=0.

fun

The function that should return "-2LLR".

MLE

The MLE of the parameter.

level

The level of the confidence. Default to 3.84 which is 95 percent confidence (assume df=1).

tol

The error bound for achieving the level given.

...

Any additional input to be passed to fun.

Author

Mai Zhou <[e-mail]>.

Details

This function just combines the two functions findUnew( ) and findLnew( ).

References

Zhao, Y., Ding, X. and Zhou (2021). Confidence Intervals of AUC and pAUC by Empirical Likelihood. Tech Report. https://www.ms.uky.edu/~mai/research/eAUC1.pdf

Examples

y <- c(10, 209, 273, 279, 324, 391, 566, 785)
x <- c(21, 38, 39, 51, 77, 185, 240, 289, 524)