bandwidth               package: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.

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)

