R: Devroye-Wise estimator

dw {alphahull} | R Documentation

## Devroye-Wise estimator

### Description

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

### Usage

    dw(x, y = NULL, eps)

### Arguments

`x, y` | The `x` and `y` arguments provide the `x` and `y` coordinates of a set of points. Alternatively, a single argument `x` can be provided, see Details.
`eps` | Value of ε.

### 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

    ## 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)

[Package alphahull version 2.2 Index]