spatstat (version 1.31-3)

unnormdensity: 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.

Value

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

Details

This is an alternative to the standard Rkernel 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 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.

See Also

density.default

Examples

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