swh:1:snp:16c54c84bc54885e783d4424d714e5cc82f479a1
Tip revision: db8668b63745f624236e566437c198010990b082 authored by Roger Koenker on 02 May 2022, 16:42:02 UTC
version 5.93
version 5.93
Tip revision: db8668b
akj.Rd
\name{akj}
\alias{akj}
\title{Density Estimation using Adaptive Kernel method}
\description{
Univariate \emph{adaptive} kernel density estimation a la Silverman.
As used by Portnoy and Koenker (1989).
}
\usage{
akj(x, z =, p =, h = -1, alpha = 0.5, kappa = 0.9, iker1 = 0)
}
\arguments{
\item{x}{points used for centers of kernel assumed to be sorted.}
\item{z}{points at which density is calculated; defaults to an
equispaced sequence covering the range of x.}
\item{p}{vector of probabilities associated with \code{x}s; defaults
to 1/n for each x.}
\item{h}{initial window size (overall); defaults to Silverman's normal
reference.}
\item{alpha}{a sensitivity parameter that determines the sensitivity of
the local bandwidth to variations in the pilot density; defaults to .5.}
\item{kappa}{constant multiplier for initial (default) window width}
\item{iker1}{integer kernel indicator: 0 for normal kernel (default)
while 1 for Cauchy kernel (\code{\link{dcauchy}}).}
}
\value{
a \code{\link{list}} structure is with components
\item{dens}{the vector of estimated density values \eqn{f(z)}}
\item{psi}{a vector of \eqn{\psi=-f'/f} function values.}
\item{score}{a vector of score \eqn{\psi' = (f'/f)^2 - f''/f} function
values.}
\item{h}{same as the input argument h}
}
\note{
if the \code{score} function values are of interest, the Cauchy kernel
may be preferable.
}
\references{
Portnoy, S and R Koenker, (1989)
Adaptive L Estimation of Linear Models;
\emph{Annals of Statistics} \bold{17}, 362--81.
Silverman, B. (1986)
\emph{Density Estimation}, pp 100--104.
}
\examples{
set.seed(1)
x <- c(rnorm(600), 2 + 2*rnorm(400))
xx <- seq(-5, 8, length=200)
z <- akj(x, xx)
plot(xx, z$dens, ylim=range(0,z$dens), type ="l", col=2)
abline(h=0, col="gray", lty=3)
plot(xx, z$psi, type ="l", col=2, main = expression(hat(psi(x))))
plot(xx, z$score, type ="l", col=2,
main = expression("score " * hat(psi) * "'" * (x)))
if(require("nor1mix")) {
m3 <- norMix(mu= c(-4, 0, 3), sig2 = c(1/3^2, 1, 2^2),
w = c(.1,.5,.4))
plot(m3, p.norm = FALSE)
set.seed(11)
x <- rnorMix(1000, m3)
z2 <- akj(x, xx)
lines(xx, z2$dens, col=2)
z3 <- akj(x, xx, kappa = 0.5, alpha = 0.88)
lines(xx, z3$dens, col=3)
}
}
\keyword{smooth}