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% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/parzen.R
\name{parzen}
\alias{parzen}
\alias{Parzen}
\title{Parzen's Kernel mode estimator}
\usage{
parzen(
x,
bw = NULL,
kernel = "gaussian",
abc = FALSE,
tolerance = .Machine$double.eps^0.25,
...
)
}
\arguments{
\item{x}{numeric. Vector of observations.}
\item{bw}{numeric. The smoothing bandwidth to be used.}
\item{kernel}{character. The kernel to be used. For available kernels see
\code{\link[statip]{densityfun}} in package \pkg{statip}.}
\item{abc}{logical. If \code{FALSE} (the default), the kernel density estimate
is maximised using \code{\link[stats]{optim}}.}
\item{tolerance}{numeric. Desired accuracy in the \code{\link[stats]{optimize}} function.}
\item{...}{If \code{abc = FALSE}, further arguments to be passed to \code{\link[stats]{optim}}.}
}
\value{
\code{parzen} returns a numeric value, the mode estimate.
If \code{abc = TRUE}, the \code{x} value maximizing the density
estimate is returned. Otherwise, the \code{\link[stats]{optim}}
method is used to perform maximization, and the attributes:
'value', 'counts', 'convergence' and 'message', coming from
the \code{\link[stats]{optim}} method, are added to the result.
}
\description{
Parzen's kernel mode estimator is the value
maximizing the kernel density estimate.
}
\details{
If \code{kernel = "uniform"}, the \code{\link[modeest]{naive}} mode estimate is returned.
}
\note{
The user may call \code{parzen} through
\code{mlv(x, method = "kernel", ...)} or \code{mlv(x, method = "parzen", ...)}.
Presently, \code{parzen} is quite slow.
}
\examples{
# Unimodal distribution
x <- rlnorm(10000, meanlog = 3.4, sdlog = 0.2)
## True mode
lnormMode(meanlog = 3.4, sdlog = 0.2)
## Estimate of the mode
mlv(x, method = "kernel", kernel = "gaussian", bw = 0.3, par = shorth(x))
}
\references{
\itemize{
\item Parzen E. (1962).
On estimation of a probability density function and mode.
\emph{Ann. Math. Stat.}, \bold{33}(3):1065--1076.
\item Konakov V.D. (1973).
On the asymptotic normality of the mode of multidimensional distributions.
\emph{Theory Probab. Appl.}, \bold{18}:794-803.
\item Eddy W.F. (1980).
Optimum kernel estimators of the mode.
\emph{Ann. Statist.}, \bold{8}(4):870-882.
\item Eddy W.F. (1982).
The Asymptotic Distributions of Kernel Estimators of the Mode.
\emph{Z. Wahrsch. Verw. Gebiete}, \bold{59}:279-290.
\item Romano J.P. (1988).
On weak convergence and optimality of kernel density estimates of the mode.
\emph{Ann. Statist.}, \bold{16}(2):629-647.
\item Abraham C., Biau G. and Cadre B. (2003).
Simple Estimation of the Mode of a Multivariate Density.
\emph{Canad. J. Statist.}, \bold{31}(1):23-34.
\item Abraham C., Biau G. and Cadre B. (2004).
On the Asymptotic Properties of a Simple Estimate of the Mode.
\emph{ESAIM Probab. Stat.}, \bold{8}:1-11.
}
}
\seealso{
\code{\link[modeest]{mlv}}, \code{\link[modeest]{naive}}
}
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