\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 }