bkfe               package:KernSmooth               R Documentation

Compute a Binned Kernel Functional Estimate

Description:

     Returns an estimate of a binned approximation to the kernel
     estimate of the specified density functional.  The kernel is the
     standard normal density.

Usage:

     bkfe(x, drv, bandwidth, gridsize = 401, range.x, binned = FALSE,
          truncate = TRUE)

Arguments:

       x: vector of observations from the distribution whose density is
          to be estimated. Missing values are not allowed. 

     drv: order of derivative in the density functional. Must be a
          non-negative even integer. 

bandwidth: the kernel bandwidth smoothing parameter.  Must be supplied. 

gridsize: the number of equally-spaced points over which binning is
          performed. 

 range.x: vector containing the minimum and maximum values of 'x' at
          which to compute the estimate. The default is the minimum and
          maximum data values, extended by the support of the kernel. 

  binned: logical flag: if 'TRUE', then 'x' and 'y' are taken to be
          grid counts rather than raw data. 

truncate: logical flag: if 'TRUE', data with 'x' values outside the
          range specified by 'range.x' are ignored. 

Details:

     The density functional of order 'drv' is the integral of the
     product of the density and its 'drv'th derivative.  The kernel
     estimates of such quantities are computed using a binned
     implementation, and the kernel is the standard normal density.

Value:

     the estimated functional.

Background:

     Estimates of this type were proposed by Sheather and Jones (1991).

References:

     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.

     Wand, M. P. and Jones, M. C. (1995). _Kernel Smoothing._ Chapman
     and Hall, London.

Examples:

     data(geyser, package="MASS")
     x <- geyser$duration
     est <- bkfe(x, drv=4, bandwidth=0.3)

