Kernel receiver operating characteristic (ROC) curve

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

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.

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 \((F_{Y_1}(z), F_{Y_2}(z))\) based on the cumulative distribution functions of \(Y_j = \bar{F}_1(\bold{X}_j), j=1,2\).

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 \(Y_j\) 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.

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)
#> Summary measures for ROC curve
#> AUC = 0.625 
#> Youden index = 0.180553 
#> (LR-, LR+) = (0.69527, 1.44307)
#> 
predict(Rhat, x=0.5) 
#> [1] 0.6736525