

   CCoommppuuttee aa BBiinnnneedd KKeerrnneell FFuunnccttiioonnaall EEssttiimmaattee

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

   AArrgguummeennttss::

          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.

   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.

     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 out-
             side the range specified by `range.x' are ignored.

   DDeessccrriippttiioonn::

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

   VVaalluuee::

        the estimated functional.

   DDeettaaiillss::

        The density functional of order `drv' is the integral
        of the product of the density and its `drv'th deriva-
        tive.  The kernel estimates of such quantities are com-
        puted using a binned implementation, and the kernel is
        the standard normal density.

   BBAACCKKGGRROOUUNNDD::

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

   RReeffeerreenncceess::

        Sheather, S. J. and Jones, M. C. (1991).  A reliable
        data-based bandwidth selection method for kernel den-
        sity 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.

   EExxaammpplleess::

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

