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.
      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:

     require(graphics)

     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)

