| smooth3vec {emplikAUC} | R Documentation |
Smoothed indicator function I[x < const], which is the integration of the Epanechnikov kernal.
Description
This function computes the smoothed Indicator function I[x < const] using a 3rd order polynomial.
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 3rd order polynomial.
eps is a scalar, must > 0. It is the smoothing window width.
Usage
smooth3vec(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 smooth3 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
smooth3vec 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)