cde.rd

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\name{cde}
\alias{cde}
\title{Conditional Density Estimation}

\description{Calculates kernel conditional density estimate using local
polynomial estimation.}

\usage{
cde(x, y, deg = 0, link = "identity", a, b, mean,
  x.margin, y.margin, x.name, y.name,
  use.locfit = FALSE, fw = TRUE, rescale = TRUE, nxmargin=15, nymargin=100, a.nndefault=0.3, ...)
}
\arguments{
  \item{x}{Numerical vector or matrix: the conditioning variable(s).}
  \item{y}{Numerical vector: the response variable.}
  \item{deg}{Degree of local polynomial used in estimation.}
  \item{link}{Link function used in estimation. Default "identity". The other possibility is "log" which is recommended if degree > 0.}
  \item{a}{Optional bandwidth in x direction.}
  \item{b}{Optional bandwidth in y direction.}
  \item{mean}{Estimated mean of y|x. If present, it will adjust conditional density to have this mean.}
  \item{x.margin}{Values in x-space on which conditional density is calculated. If not specified, an equi-spaced grid of \code{nxmargin} values over the range of x is used.
	If x is a matrix, x.margin should be a list of two numerical vectors.}
  \item{y.margin}{Values in y-space on which conditional density is calculated. If not specified, an equi-spaced grid of \code{nymargin} values over the range of y is used.}
  \item{x.name}{Optional name of x variable used in plots.}
  \item{y.name}{Optional name of y variable used in plots.}
  \item{use.locfit}{If TRUE, will use \code{\link[locfit]{locfit}} for estimation. Otherwise \code{\link[base]{ksmooth}}
  is used. \code{\link[locfit]{locfit}} is used if degree>0 or link not the identity or the dimension of x is
   greater than 1 even if \code{use.locfit=FALSE}.}
  \item{fw}{If TRUE (default), will use fixed window width estimation. Otherwise nearest neighbourhood estimation is used. If the dimension of x is greater than 1, nearest neighbourhood must be used.}
  \item{rescale}{If TRUE (default), will rescale the conditional densities to integrate to one.}
  \item{nxmargin}{Number of values used in \code{x.margin} by default.}
  \item{nymargin}{Number of values used in \code{y.margin} by default.}
  \item{a.nndefault}{Default nearest neighbour bandwidth (used only if \code{fw=FALSE} and \code{a} is missing.).}
  \item{\dots}{Additional arguments are passed to locfit.}
}
\value{A list with the following components:
  \item{x}{grid in x direction on which density evaluated. Equal to x.margin if specified.}
  \item{y}{grid in y direction on which density is evaluated. Equal to y.margin if specified. }
  \item{z}{value of conditional density estimate returned as a matrix. }
  \item{a}{window width in x direction.}
  \item{b}{window width in y direction.}
  \item{x.name}{Name of x variable to be used in plots.}
  \item{y.name}{Name of y variable to be used in plots.}
}

\details{If bandwidths are omitted, they are computed using normal
reference rules described in Bashtannyk and Hyndman (2001) and
Hyndman and Yao (2002). Bias adjustment uses the method described in
Hyndman, Bashtannyk and Grunwald (1996). If deg>1 then estimation is
based on the local parametric estimator of Hyndman and Yao (2002).}

\references{Hyndman, R.J., Bashtannyk, D.M. and Grunwald, G.K. (1996)
"Estimating and visualizing conditional densities". \emph{Journal of
Computational and Graphical Statistics}, \bold{5}, 315-336.

Bashtannyk, D.M., and Hyndman, R.J. (2001) "Bandwidth selection for kernel
conditional density estimation". \emph{Computational statistics and data
analysis}, \bold{36}(3), 279-298.

Hyndman, R.J. and Yao, Q. (2002) "Nonparametric estimation and symmetry tests
for conditional density functions". \emph{Journal of Nonparametric Statistics},
\bold{14}(3), 259-278.}


\author{Rob Hyndman}

\seealso{\code{\link{cde.bandwidths}}}
\examples{
# Old faithful data
faithful.cde <- cde(faithful$waiting, faithful$eruptions,
	x.name="Waiting time", y.name="Duration time")
plot(faithful.cde)
plot(faithful.cde, plot.fn="hdr")

# Melbourne maximum temperatures with bias adjustment
x <- maxtemp[1:3649]
y <- maxtemp[2:3650]
maxtemp.cde <- cde(x,y,
	x.name="Today's max temperature",y.name="Tomorrow's max temperature")
# Assume linear mean
fit <- lm(y~x)
fit.mean <- list(x=6:45,y=fit$coef[1]+fit$coef[2]*(6:45))
maxtemp.cde2 <- cde(x,y,mean=fit.mean,
	x.name="Today's max temperature",y.name="Tomorrow's max temperature")
plot(maxtemp.cde)
}
\keyword{smooth}
\keyword{distribution}
\keyword{hplot}