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

```
kroc(x1, x2, H1, h1, hy, gridsize, gridtype, xmin, xmax, supp=3.7, eval.points,
binned=FALSE, bgridsize, positive=FALSE, adj.positive, w, verbose=FALSE)
```# S3 method for kroc
predict(object, ..., x)
# S3 method for kroc
summary(object, ...)

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. Default is FALSE.

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

A kernel ROC curve is an object of class `kroc`

which is a list
with fields:

list of data values `x1, x2`

- same as input

vector or list of points at which the estimate is evaluated

ROC curve estimate at `eval.points`

"linear"

flag for estimation on a grid

flag for binned estimation

variable names

weights

"lower.tail"

scalar bandwidth for first sample (1-d only)

bandwidth matrix for first sample

scalar bandwidth for ROC curve

summary indices of ROC curve.

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.

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.

```
# NOT RUN {
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)
# }
```

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