bw.abram.net: Abramson's adaptive bandwidth for networks

In kernstadapt: Adaptive Kernel Estimators for Point Process Intensities on Linear Networks

Abramson's adaptive bandwidth for networks

Description

Computes adaptive smoothing bandwidth in the network case according to the inverse-square-root rule of Abramson (1982).

Usage

## S3 method for class 'net'
bw.abram(
  X,
  h0,
  ...,
  at = c("points", "pixels"),
  hp = h0,
  pilot = NULL,
  trim = 5,
  smoother = densityQuick.lpp
)

Arguments

X	A point pattern on a linear network (object of class "lpp").
h0	The global smoothing bandwidth. The default is the maximal oversmoothing principle of Terrell (1990).
...	Additional arguments passed to smoother to control the type of smoothing.
at	Character string specifying whether to compute bandwidths at the points (at = "points", the default) or to compute bandwidths at every bin in a bin grid (at = "bins").
hp	Optional. A scalar pilot bandwidth, used for estimation of the pilot density if required.
pilot	Optional. A pilot estimation of the intensity to plug in Abramson's formula.
trim	A trimming value to cut extreme large bandwidths.
smoother	Smoother for the pilot. A function or character string, specifying the function to be used to compute the pilot estimate when pilot is NULL or is a point pattern.

Details

This function returns a set of adaptive smoothing bandwidths driven by Abramson's (1982) method for a point pattern in a linear network. The bandwidth at location u is given by

\epsilon(u) = h0 * \mbox{min}\left[ \frac{1}{\gamma} \sqrt{\frac{n}{\tilde{lambda}(u)}}, \mbox{\texttt{trim}} \right]

where \tilde{\lambda}(u) is a pilot estimate of the network varying intensity and \gamma is a scaling constant depending on the pilot estimate.

Value

If at = "points" (the default), the result is a numeric vector with one bandwidth for each data point in X. If at = "pixels", the output is an object with class "linim"

Author(s)

Jonatan A. González

References

Abramson, I. (1982) On bandwidth variation in kernel estimates — a square root law. Annals of Statistics, 10(4), 1217-1223.

Examples

#To be done

kernstadapt documentation built on Sept. 30, 2024, 9:44 a.m.