R: Weighted kernel smoother

unnormdensity {spatstat.geom} | R Documentation

## Weighted kernel smoother

### Description

An unnormalised version of kernel density estimation where the weights are not required to sum to 1. The weights may be positive, negative or zero.

### Usage

    unnormdensity(x, ..., weights = NULL)

### Arguments

`x` | Numeric vector of data
`...` | Arguments passed to `density.default`. Arguments must be named.

'

`weights` | Optional numeric vector of weights for the data.

### Details

This is an alternative to the standard R kernel density estimation function `density.default`.

The standard `density.default` requires the `weights` to be nonnegative numbers that add up to 1, and returns a probability density (a function that integrates to 1).

This function `unnormdensity` does not impose any requirement on the `weights` except that they be finite. Individual weights may be positive, negative or zero. The result is a function that does not necessarily integrate to 1 and may be negative. The result is the convolution of the kernel k with the weighted data,

f(x) = sum of w[i] * k(x - x[i])

where x[i] are the data points and w[i] are the weights.

The algorithm first selects the kernel bandwidth by applying `density.default` to the data `x` with normalised, positive weight vector `w = abs(weights)/sum(abs(weights))` and extracting the selected bandwidth. Then the result is computed by applying applying `density.default` to `x` twice using the normalised positive and negative parts of the weights.

Note that the arguments `...` must be passed by name, i.e. in the form (`name=value`). Arguments that do not match an argument of `density.default` will be ignored silently.

### Value

Object of class `"density"` as described in `density.default`.

### Author(s)

Adrian Baddeley Adrian.Baddeley@curtin.edu.au

and Rolf Turner r.turner@auckland.ac.nz

### See Also

`density.default`

### Examples

      d <- unnormdensity(1:3, weights=c(-1,0,1))
      if(interactive()) plot(d)

[Package spatstat.geom version 2.2-0 Index]