| smooth3 {emplikAUC} | R Documentation |
Smoothed indicator function I[x < y], which is the integration of the Epanechnikov kernal.
Description
This function computes the smoothed Indicator function I[x < y] using a 3rd order polynomial.
If |x-y| > eps then the result is the same as the indicator function I[x < y] (either 0 or 1). For |x-y| < eps, it is a 3rd order polynomial.
eps is a scalar, must > 0. It is the smoothing window width.
Usage
smooth3(x, y, eps=0.05)
Arguments
x |
a vector of observations, length m, for the first sample. |
y |
a vector of observations, length n, for the second sample. |
eps |
The smoothing window width, must >0. |
Details
This function is used in many places to replace an indicator function I[x<y].
For example, when estimating the AUC.
It is listed here because users may find it useful elsewhere.
Value
smooth3( ) returns a matrix of dimension ncol=length(y), nrow=length(x). The entry
of the matrix are smoothed values of I[x[i] < y[j]].
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)