| smoothLvec {emplikAUC} | R Documentation |
Smoothed indicator function I[x < const], linear connecting the 1 and 0 on [-eps, eps].
Description
This function computes the smoothed Indicator function I[x < const] using a liare.
If |x - const| > eps then the result is the same as the indicator function I[x < const] (either 0 or 1). For |x - const| < eps, it is a linear function.
eps is a scalar, must > 0. It is the smoothing window width.
Usage
smoothLvec(x, const, eps=0.05)
Arguments
x |
a vector of observations, length m, for the first sample. |
const |
a single number. |
eps |
The smoothing window width, must be >0. Ideally this should be sample size dependent. |
Details
This function is similar to smooth3vec but only compare the x vector to a single number
and thus returns a vector instead of matrix.
You may also use the smooth3() with a bit care, for that matter, but this vector
version should be faster and save memory.
It is listed here because the user may find it useful elsewhere.
We used this function to estimate the quantile from the x-sample.
Value
smoothLvec returns a vector of length=length(x). The entry
of the vector are smoothed values of I[x[i] < const].
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)