Last data update: 2014.03.03
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R: Density Estimation using Adaptive Kernel method
Density Estimation using Adaptive Kernel method
Description
Univariate 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
x |
points used for centers of kernel assumed to be sorted.
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z |
points at which density is calculated; defaults to an
equispaced sequence covering the range of x.
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p |
vector of probabilities associated with x s; defaults
to 1/n for each x.
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h |
initial window size (overall); defaults to Silverman's normal
reference.
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alpha |
a sensitivity parameter that determines the sensitivity of
the local bandwidth to variations in the pilot density; defaults to .5.
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kappa |
constant multiplier for initial (default) window width
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iker1 |
integer kernel indicator: 0 for normal kernel (default)
while 1 for Cauchy kernel (dcauchy ).
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Value
a list structure is with components
dens |
the vector of estimated density values f(z)
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psi |
a vector of ψ=-f'/f function values.
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score |
a vector of score ψ' = (f'/f)^2 - f''/f function
values.
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h |
same as the input argument h
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Note
if the 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;
Annals of Statistics 17, 362–81.
Silverman, B. (1986)
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)
}
Results
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