# Devroye-Wise estimator

### Description

This function calculates the Devroye-Wise estimator of a given sample of points in the plane for *ε>0*.

### Usage

1 |

### Arguments

`x, y` |
The |

`eps` |
Value of |

### Details

An attempt is made to interpret the arguments x and y in a way suitable for computing the Devroye-Wise estimator. Any reasonable way of defining the coordinates is acceptable, see `xy.coords`

.

### Value

Given a sample of points in the plane, the estimator is defined as union of balls of radius *ε* with centers in the sample points. For each arc in the boundary of the Devroye-Wise estimator, the columns of the output matrix store the center *c* and radius *r* of the arc, the unitary vector *v*, the angle *θ* that define the arc and the indices of the end points.

### References

Devroye, L. and Wise, G. (1980) Detection of abnormal behaviour via nonparametric estimation of the support. *SIAM J. Appl. Math.* 3, pp. 480-488.

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 | ```
## Not run:
# Uniform sample of size n = 200 in the annulus B(c, 0.5)\B(c, 0.25),
# with c = (0.5, 0.5).
n <- 200
theta <- runif(n, 0, 2*pi)
r <- sqrt(runif(n, 0.25^2, 0.5^2))
x <- cbind(0.5 + r*cos(theta), 0.5 + r*sin(theta))
eps <- 0.05
dw.obj <- dw(x, eps = eps)
plot(x)
for(i in 1:dim(dw.obj)[1]){arc(dw.obj[i, 1:2], eps, dw.obj[i, 4:5], dw.obj[i, 6])}
## End(Not run)
``` |