unnormdensity: Weighted kernel smoother

In spatstat.geom: Geometrical Functionality of the 'spatstat' Family

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, defaults)

Arguments

x	Numeric vector of data
...	Optional arguments passed to density.default. Arguments must be named.

'

weights	Optional numeric vector of weights for the data. The default is equivalent to assuming a weight of 1 for each observation.
defaults	Optional, named list of arguments passed to density.default. These will be overridden by arguments in ....

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_i w_i k(x- x_i)

where x_i are the data points and w_i are the weights.

The argument weights should be a numeric vector of the same length as x, or a single numeric value. The default is to assume a weight of 1 for each observation in x.

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.

Warning

If weights is not specified, the default is to assign a weight w_i=1 to each observation x_i.

This is not the same behaviour as in density.default which effectively assumes a weight of 1/n for each observation x_i where n=length(x).

Author(s)

\adrian

and \rolf

See Also

density.default

Examples

  d <- unnormdensity(1:3, weights=c(-1,0,1), bw=0.3)
  if(interactive()) plot(d)

spatstat.geom documentation built on Oct. 20, 2023, 9:06 a.m.