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kroc

Kernel receiver operating characteristic (ROC) curve

Description

Kernel receiver operating characteristic (ROC) curve for 1- to 3-dimensional data.

Usage

kroc(x1, x2, H1, h1, hy, gridsize, gridtype, xmin, xmax, supp=3.7, eval.points,
   binned, bgridsize, positive=FALSE, adj.positive, w, verbose=FALSE)

## S3 method for class 'kroc'
predict(object, ..., x)
## S3 method for class 'kroc'
summary(object, ...)

Arguments

`x,x1,x2`	vector/matrix of data values
`H1,h1,hy`	bandwidth matrix/scalar bandwidths. If these are missing, `Hpi.kcde`, `hpi.kcde` is called by default.
`gridsize`	vector of number of grid points
`gridtype`	not yet implemented
`xmin,xmax`	vector of minimum/maximum values for grid
`supp`	effective support for standard normal
`eval.points`	not yet implemented
`binned`	flag for binned estimation
`bgridsize`	vector of binning grid sizes
`positive`	flag if 1-d data are positive. Default is FALSE.
`adj.positive`	adjustment applied to positive 1-d data
`w`	vector of weights. Default is a vector of all ones.
`verbose`	flag to print out progress information. Default is FALSE.
`object`	object of class `kroc`, output from `kroc`
`...`	other parameters

Details

In this set-up, the values in the first sample x1 should be larger in general that those in the second sample x2. The usual method for computing 1-d ROC curves is not valid for multivariate data. Duong (2014), based on Lloyd (1998), develops an alternative formulation (F_Y1(z), F_Y2(z)) based on the cumulative distribution functions of Yj=bar(F)_1(Xj), j=1,2.

If the bandwidth H1 is missing from kroc, then the default bandwidth is the plug-in selector Hpi.kcde. Likewise for missing h1,hy. A bandwidth matrix H1 is required for x1 for d>1, but the second bandwidth hy is always a scalar since Yj are 1-d variables.

The effective support, binning, grid size, grid range, positive parameters are the same as kde.

–The summary method for kroc objects prints out the summary indices of the ROC curve, as contained in the indices field, namely the AUC (area under the curve) and Youden index.

Value

A kernel ROC curve is an object of class kroc which is a list with fields:

`x`	list of data values `x1, x2` - same as input
`eval.points`	vector or list of points at which the estimate is evaluated
`estimate`	ROC curve estimate at `eval.points`
`gridtype`	"linear"
`gridded`	flag for estimation on a grid
`binned`	flag for binned estimation
`names`	variable names
`w`	vector of weights
`tail`	"lower.tail"
`h1`	scalar bandwidth for first sample (1-d only)
`H1`	bandwidth matrix for first sample
`hy`	scalar bandwidth for ROC curve
`indices`	summary indices of ROC curve.

References

Duong, T. (2016) Non-parametric smoothed estimation of multivariate cumulative distribution and survival functions, and receiver operating characteristic curves. Journal of the Korean Statistical Society, 45, 33-50.

Lloyd, C. (1998) Using smoothed receiver operating curves to summarize and compare diagnostic systems. Journal of the American Statistical Association, 93, 1356-1364.

Examples

samp <- 1000
x <- rnorm.mixt(n=samp, mus=0, sigmas=1, props=1)
y <- rnorm.mixt(n=samp, mus=0.5, sigmas=1, props=1)
Rhat <- kroc(x1=x, x2=y)
summary(Rhat)
predict(Rhat, x=0.5)

ks

Kernel Smoothing

v1.12.0

GPL-2 | GPL-3

Authors

Tarn Duong [aut, cre], Matt Wand [ctb], Jose Chacon [ctb], Artur Gramacki [ctb]

Initial release

2021-02-06