cenROC (version 2.0.0)

CV: The cross-validation bandwidth selection for weighted data

Description

This function computes the data-driven bandwidth for smoothing the ROC (or distribution) function using the CV method of Beyene and El Ghouch (2020). This is an extension of the classical (unweighted) cross-validation bandwith selection method to the case of weighted data.

Usage

CV(X, wt, ktype = "normal")

Value

Returns the computed value for the bandwith parameter.

Arguments

X

The numeric data vector.

wt

The non-negative weight vector.

ktype

A character string giving the type kernel to be used: "normal", "epanechnikov", "biweight", or "triweight". By default, the "normal" kernel is used.

Author

Kassu Mehari Beyene and Anouar El Ghouch

Details

Bowman et al (1998) proposed the cross-validation bandwidth selection method for unweighted kernal smoothed distribution function. This method is implemented in the R package kerdiest. We adapted this for the case of weighted data by incorporating the weight variable into the cross-validation function of Bowman's method. See Beyene and El Ghouch (2020) for details.

References

Beyene, K. M. and El Ghouch A. (2020). Smoothed time-dependent receiver operating characteristic curve for right censored survival data. Statistics in Medicine. 39: 3373– 3396.

Bowman A., Hall P. and Trvan T.(1998). Bandwidth selection for the smoothing of distribution functions. Biometrika 85:799-808.

Quintela-del-Rio, A. and Estevez-Perez, G. (2015). kerdiest: Nonparametric kernel estimation of the distribution function, bandwidth selection and estimation of related functions. R package version 1.2.

Examples

library(cenROC)

X <- rnorm(100) # random data vector
wt <- runif(100) # weight vector

## Cross-validation bandwidth selection
CV(X = X, wt = wt)$bw