emplikAUC (version 0.5)

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

Description

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

Usage

findUnew(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

Up

Upper bound of the confidence interval.

FstepU

The error when search for Upper bound.

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 user supplied function that should return "-2LLR".

MLE

The MLE of the parameter. An approximate value should be OK.

level

The level of the confidence. Default to 3.84 which is 95 percent confidence.

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 is similar to findLnew( ).

The search is separate (for upper and lower) since Upper and Lower bound may behave differently and require different nuisance parameters inputs (in ...).

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)