Handles univariate non-parametric density estimation with
parametric starts and asymmetric kernels in a simple and flexible way.
Kernel density estimation with parametric starts involves fitting a
parametric density to the data before making a correction with kernel
density estimation, see Hjort & Glad (1995)
R package for univariate kernel density estimation with parametric
starts and asymmetric kernels.
kdensity is an implementation of univariate kernel density estimation
with support for parametric starts and asymmetric kernels. Its main
kdensity, which is has approximately the same syntax as
stats::density. Its new functionality is:
kdensityhas built-in support for many parametric starts, such as
gamma, but you can also supply your own.
gammakernels, but also the common symmetric ones. In addition, you can also supply your own kernels.
bw, again including an option to specify your own.
A reason to use
kdensity is to avoid boundary bias when estimating
densities on the unit interval or the positive half-line. Asymmetric
kernels such as
gcopula are designed for this purpose. The
support for parametric starts allows you to easily use a method that is
often superior to ordinary kernel density estimation.
First you need to install the package
R, use the following command.
This installs the latest version of the package from GitHub. Call the
library function and use it just like
stats:density, but with
optional additional arguments.
library("kdensity")plot(kdensity(mtcars$mpg, start = "normal"))
Kernel density estimation with a parametric start was introduced by Hjort and Glad in Nonparametric Density Estimation with a Parametric Start (1995). The idea is to start out with a parametric density before you do your kernel density estimation, so that your actual kernel density estimation will be a correction to the original parametric estimate. This is a good idea because the resulting estimator will be better than an ordinary kernel density estimator whenever the true density is close to your suggestion; and the estimator can be superior to the ordinary kernal density estimator even when the suggestion is pretty far off.
In addition to parametric starts, the package implements some asymmetric kernels. These kernels are useful when modelling data with sharp boundaries, such as data supported on the positive half-line or the unit interval. Currently we support the following asymmetric kernels:
Jones and Henderson’s Gaussian copula KDE, from Kernel-Type
Density Estimation on the Unit Interval
This is used for data on the unit interval. The bandwidth selection
mechanism described in that paper is implemented as well. This
kernel is called
Chen’s two beta kernels from Beta kernel estimators for density
These are used for data supported on the on the unit interval, and
Chen’s two gamma kernels from Probability Density Function
Estimation Using Gamma Kernels
These are used for data supported on the positive half-line, and are
These features can be combined to make asymmetric kernel densities
estimators with parametric starts, see the example below. The package
contains only one function,
kdensity, in addition to the generics
kdensity takes some
data, a kernel
kernel and a
start. You can optionally specify the
parameter, which is used to find the normalizing constant.
The following example uses the data set plots both a gamma-kernel density estimate with a gamma start (black) and the the fully parametric gamma density. The underlying parameter estimates are always maximum likelood.
library("kdensity")kde = kdensity(airquality$Wind, start = "gamma", kernel = "gamma")plot(kde, main = "Wind speed (mph)")lines(kde, plot_start = TRUE, col = "red")rug(airquality$Wind)
Since the return value of
kdensity is a function, it is callable, as
kde(10)#>  0.09980471
You can access the parameter estimates by using
coef. You can also
access the log likelihood (
logLik), AIC and BIC of the parametric
coef(kde)#> shape rate#> 7.1872898 0.7217954logLik(kde)#> 'log Lik.' 12.33787 (df=2)AIC(kde)#>  -20.67574