sjpi: Sheather-Jones Plug-in bandwidth criterion.

Description

Given a dataset and set of pilot bandwidths, this function computes a bandwidth via the plug-in method, and the assumed `pilot' relationship of Sheather and Jones (1991). The S-J method chooses the bandwidth at which the two intersect.

The purpose of this function is to demonstrate the sensitivity of plug-in methods to pilot bandwidths and assumptions. This function does not provide a reliable method of bandwidth selection.

Usage

sjpi(x, a)

Value

A matrix with four columns; the number of rows equals the length of a. The first column is the plug-in selected bandwidth. The second column is the pilot bandwidths a. The third column is the pilot bandwidth according to the assumed relationship of Sheather and Jones. The fourth column is an intermediate calculation.

Arguments

x: data vector
a: vector of pilot bandwidths

References

Sheather, S. J. and Jones, M. C. (1991). A reliable data-based bandwidth selection method for kernel density estimation. JRSS-B 53, 683-690.

Examples

Run this code

# Fig 10.2 (S-J parts) from Loader (1999).
data(geyser, package="locfit")
gf <- 2.5
a <- seq(0.05, 0.7, length=100)
z <- sjpi(geyser, a)

# the plug-in curve. Multiplying by gf=2.5 corresponds to Locfit's standard
# scaling for the Gaussian kernel.
plot(gf*z[, 2], gf*z[, 1], type = "l", xlab = "Pilot Bandwidth k", ylab
     = "Bandwidth h")

# Add the assumed curve.
lines(gf * z[, 3], gf * z[, 1], lty = 2)
legend(gf*0.05, gf*0.4, lty = 1:2, legend = c("Plug-in", "SJ assumed"))