Computes the integral of the squared kernel,
for the kernels used in density estimation
for numerical data.
Usage
kernel.squint(kernel = "gaussian", bw=1)
Arguments
kernel
String name of the kernel.
Options are
"gaussian", "rectangular",
"triangular",
"epanechnikov",
"biweight",
"cosine" and "optcosine".
(Partial matching is used).
bw
Bandwidth (standard deviation) of the kernel.
Value
A single number.
Details
Kernel estimation of a probability density in one dimension
is performed by density.default
using a kernel function selected from the list above.
This function computes the integral of the squared kernel,
$$
R = \int_{-\infty}^{\infty} k(x)^2 \, {\rm d}x
$$
where $k(x)$ is the kernel with bandwidth bw.
kernel.squint("gaussian", 3)
# integral of squared Epanechnikov kernel with half-width h=1 h <- 1
bw <- h/kernel.factor("epa")
kernel.squint("epa", bw)