Bandwidth Selectors for Kernel Density Estimation

andwidth(stats) R Documentation
Bandwidth Selectors for Kernel Density Estimation
Description
Bandwidth selectors for gaussian windows in density.
Usage
bw.nrd0(x)
bw.nrd(x)
bw.ucv(x, nb = 1000, lower = 0.1 * hmax, upper = hmax)
bw.bcv(x, nb = 1000, lower = 0.1 * hmax, upper = hmax)
bw.SJ(x, nb = 1000, lower = 0.1 * hmax, upper = hmax,
method = c("ste", "dpi"))
Arguments
x A data vector.
nb number of bins to use.
lower,
upper
Range over which to minimize. The default is almost always satisfactory. hmax is
calculated internally from a normal reference bandwidth.
method Either "ste" ("solve-the-equation") or "dpi" ("direct plug-in").
Details
bw.nrd0 implements a rule-of-thumb for choosing the bandwidth of a Gaussian kernel density
estimator. It defaults to 0.9 times the minimum of the standard deviation and the interquartile
range divided by 1.34 times the sample size to the negative one-fifth power (= Silverman's
“rule of thumb”, Silverman (1986, page 48, eqn (3.31)) unless the quartiles coincide when a
positive result will be guaranteed.
bw.nrd is the more common variation given by Scott (1992), using factor 1.06.
bw.ucv and bw.bcv implement unbiased and biased cross-validation respectively.
bw.SJ implements the methods of Sheather & Jones (1991) to select the bandwidth using pilot
estimation of derivatives.
The algorithm solves an equation (via uniroot) and because of that, enlarges the interval
c(lower,upper) when the boundaries were not user-specified and do not bracket the root.
Value
A bandwidth on a scale suitable for the bw argument of density.

References
Scott, D. W. (1992) Multivariate Density Estimation: Theory, Practice, and Visualization.
Wiley.
Sheather, S. J. and Jones, M. C. (1991) A reliable data-based bandwidth selection method for
kernel density estimation. Journal of the Royal Statistical Society series B, 53, 683–690.
Silverman, B. W. (1986) Density Estimation. London: Chapman and Hall.
Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Springer.
See Also
density.
bandwidth.nrd, ucv, bcv and width.SJ in package MASS, which are all scaled to the width
argument of density and so give answers four times as large.
Examples
plot(density(precip, n = 1000))
rug(precip)
lines(density(precip, bw="nrd"), col = 2)
lines(density(precip, bw="ucv"), col = 3)
lines(density(precip, bw="bcv"), col = 4)
lines(density(precip, bw="SJ-ste"), col = 5)
lines(density(precip, bw="SJ-dpi"), col = 6)
legend(55, 0.035,
legend = c("nrd0", "nrd", "ucv", "bcv", "SJ-ste", "SJ-dpi"),
col = 1:6, lty = 1)
[Package stats version 2.5.1 Index]