| bandwidth {stats} | R Documentation |
Bandwidth selectors for gaussian windows in density.
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"))
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"). |
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.
A bandwidth on a scale suitable for the bw argument
of density.
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.
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.
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)