smooth3: Smoothed indicator function I[x < y], which is the...

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

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 <[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.