smooth5vec: Smoothed indicator function I[x < const], which is the...

In emplikAUC: Empirical Likelihood Ratio Test/Confidence Interval for AUC or pAUC

Smoothed indicator function I[x < const], which is the integration of the Quartic kernal.

Description

This function computes the smoothed Indicator function I[x < const] using a 5th 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 5th order polynomial.

eps is a scalar, must > 0. It is the smoothing window width.

Usage

smooth5vec(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 twice continuously differenciable, smoother than smooth3vec. It is listed here because the user may need extra smoothness (compare to smooth3vec) and may find it useful elsewhere.

Value

smooth5vec returns a vector of length=length(x). The entry of the vector are smoothed values of I[x[i] < const].

Author(s)

Mai Zhou <[e-mail]>.

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)

emplikAUC documentation built on June 22, 2024, 9:18 a.m.