kda.rd

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\name{kda, Hkda, Hkda.diag, hkda}
\alias{Hkda}
\alias{Hkda.diag}
\alias{kda}
\alias{hkda}

\title{Kernel discriminant analysis for multivariate data}
\description{
  Kernel discriminant analysis for 1- to 6-dimensional data.
}
\usage{
Hkda(x, x.group, Hstart, bw="plugin", nstage=2, pilot="samse",
     pre="sphere", binned=FALSE, bgridsize)
Hkda.diag(x, x.group, bw="plugin", nstage=2, pilot="samse", 
     pre="sphere", binned=FALSE, bgridsize)
hkda(x, x.group, bw="plugin", nstage=2, binned=TRUE, bgridsize)

kda(x, x.group, Hs, hs, y, prior.prob=NULL)
}

\arguments{
  \item{x}{matrix of training data values}
  \item{x.group}{vector of group labels for training data}
  \item{y}{matrix of test data} 
  \item{Hs}{(stacked) matrix of bandwidth matrices}
  \item{hs}{vector of scalar bandwidths}
  \item{prior.prob}{vector of prior probabilities}
  \item{bw}{bandwidth: \code{"plugin"} = plug-in, \code{"lscv"} = LSCV, 
    \code{"scv"} = SCV} 
  \item{nstage}{number of stages in the plug-in bandwidth selector (1 or 2)}
  \item{pilot}{\code{"amse"} = AMSE pilot bandwidths,
    \code{"samse"} = single SAMSE pilot bandwidth}
  \item{pre}{\code{"scale"} = pre-scaling, \code{"sphere"} =
    pre-sphering}
  \item{Hstart}{(stacked) matrix of initial bandwidth matrices, used in
    numerical optimisation}
    \item{binned}{flag for binned kernel estimation}
  \item{bgridsize}{vector of binning grid sizes - 
  required only if \code{binned=TRUE}}
}

\value{
  -- The result from \code{Hkda} and \code{Hkda.diag} is a stacked matrix
  of bandwidth matrices, one for each training data group. The result
  from \code{hkda} is a vector of bandwidths, one for each training data
  group.  

  -- The result from \code{kda} is a vector of group labels
  estimated via the kernel discriminant rule.  If the test data \code{y} are
  given then these are classified. Otherwise the training data \code{x}
  are classified.
}

\references{
  Mardia, K.V., Kent, J.T. \& Bibby J.M. (1979) \emph{Multivariate
    Analysis}. Academic Press. London.
 
  Silverman, B. W. (1986) \emph{Data Analysis for Statistics and Data
    Analysis}. Chapman \& Hall. London.
  
  Simonoff, J. S. (1996) \emph{Smoothing Methods in Statistics}.
  Springer-Verlag. New York

  Venables, W.N. & Ripley, B.D. (1997) \emph{Modern Applied Statistics with
    S-PLUS}. Springer-Verlag. New York.   
}

\details{
  -- The values that valid for \code{bw} are \code{"plugin", "lscv"} and
  \code{"scv"} for
  \code{Hkda}.  These in turn call \code{\link{Hpi}},
  \code{\link{Hlscv}} and \code{\link{Hscv}}. For plugin selectors, all
  of \code{nstage}, \code{pilot} and \code{pre} need to be set. For SCV
  selectors, currently \code{nstage=1} always but \code{pilot} and \code{pre}
  need to be set.  For LSCV selectors, none of them are required. 
  \code{Hkda.diag} makes analagous calls to diagonal selectors.

  For d = 1, 2, 3, 4, 
  and if \code{eval.points} is not specified, then the
  density estimate is computed over a grid 
  defined by \code{gridsize} (if \code{binned=FALSE}) or
  by \code{bgridsize} (if \code{binned=TRUE}).
  
  For d = 1, 2, 3, 4, 
  and if \code{eval.points} is specified, then the
  density estimate is computed exactly at \code{eval.points}.
  
  For d > 4, the kernel density estimate is computed exactly 
  and \code{eval.points} must be specified.
  
  For details on the pre-transformations in \code{pre}, see
  \code{\link{pre.sphere}} and \code{\link{pre.scale}}.

  -- If you have prior probabilities then set \code{prior.prob} to these.
  Otherwise \code{prior.prob=NULL} is the default i.e. use the sample
  proportions as estimates of the prior probabilities.
}

\seealso{
  \code{\link{compare}}, 
  \code{\link{compare.kda.cv}},
  \code{\link{kda.kde}}
}

\examples{ ### See examples in ? plot.kda.kde } 

\keyword{ smooth }