# Kernel receiver operating characteristic (ROC) curve

### Description

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

### Usage

1 2 3 4 5 6 7 |

### Arguments

`x,x1,x2` |
vector/matrix of data values |

`H1,h1,hy` |
bandwidth matrix/scalar bandwidths. If these are
missing, |

`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 |

`...` |
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`

.

â€“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 |

`eval.points` |
points at which the estimate is evaluated |

`estimate` |
ROC curve estimate at |

`gridtype` |
"linear" |

`gridded` |
flag for estimation on a grid |

`binned` |
flag for binned estimation |

`names` |
variable names |

`w` |
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. (2015) Non-parametric smoothed estimation of multivariate
cumulative distribution and survival functions, and receiver operating
characteristic curves. *Journal of the Korean Statistical
Society*. In press. DOI:10.1016/j.jkss.2015.06.002.

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

### See Also

`kcde`

### Examples

1 2 3 4 5 6 | ```
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)
``` |