| EL2paucT1T2 {emplikAUC} | R Documentation |
Testing one pAUC(p1, p2) and two quantile values together by Empirical Likelihood.
Description
This function computes the two sample Log Empirical Likelihood ratio
for testing H_0: pAUC(p1, p2) = theta; F(tau1)=1-p2; F(tau2)= 1-p1.
The two samples are in the x-vector and y-vector.
Usage
EL2paucT1T2(tauVec, pauc, partial1, partial2, x, y, epsxy)
Arguments
tauVec |
The vector (tau1, tau2), the two quantile values, to be tested. |
pauc |
The value of the pAUC(p1, p2) under |
partial1 |
The probability that define the quantile 1 |
partial2 |
The probability that define the quantile 2. Must satisfy partial 1 < partial 2 . |
x |
a vector of observations, length m, for the first sample. |
y |
a vector of observations, length n, for the second sample. |
epsxy |
The parameter for smoothing when compare x-y. |
Details
The input tauVec=(tau1, tau2), and must have: tau1 < tau2. The relavant definitions are:
tau1 = F^{-1}(1-partial2); tau2 = F^{-1}(1-partial1).
Thus, we must have partial2 > partial1.
This function is testing 3 parameters simultanuously.
It depend on the package emplik2.
The empirical likelihood we used here is defined as
EL = \prod_{i=1}^m v_i \prod_{j=1}^n \nu_j ~;~~~s.t. ~~~~~ \sum v_i =1 ~,~~ \sum \nu_j =1 ~.
Value
A single value that is the "-2LLR" from emplik2::el2.cen.EMm().
Typically should be distributed as chi square df=3, under H_0.
Author(s)
Mai Zhou <maizhou@gmail.com>.
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)