kernel.conv | R Documentation |
The (S3) generic function kernel.conv
computes the convolution
of r'th derivative for kernel function.
kernel.conv(x, ...)
## Default S3 method:
kernel.conv(x = NULL, deriv.order = 0,kernel = c("gaussian","epanechnikov",
"uniform", "triangular", "triweight", "tricube",
"biweight", "cosine", "silverman"), ...)
x |
points at which the convolution of kernel derivative is to be evaluated. |
deriv.order |
derivative order (scalar). |
kernel |
a character string giving the smoothing kernel to be used,
with default |
... |
further arguments for (non-default) methods. |
The convolution of r'th derivative for kernel function is written K^{(r)}\ast K^{(r)}
. It is defined as
the integral of the product of the derivative for kernel. As such, it is a particular kind of integral transform:
K^{(r)} \ast K^{(r)}(x) = \int_{-\infty}^{+\infty} K^{(r)}(y)K^{(r)}(x-y)dy
where:
K^{(r)}(x) = \frac{d^{r}}{d x^{r}} K(x)
for r = 0, 1, 2, \dots
kernel |
name of kernel to use. |
deriv.order |
the derivative order to use. |
x |
the n coordinates of the points where the convolution of kernel derivative is evaluated. |
kx |
the convolution of kernel derivative values. |
Arsalane Chouaib Guidoum acguidoum@usthb.dz
Olver, F. W., Lozier, D. W., Boisvert, R. F. and Clark, C. W. (2010). NIST Handbook of Mathematical Functions. Cambridge University Press, New York, USA.
Scott, D. W. (1992). Multivariate Density Estimation. Theory, Practice and Visualization. New York: Wiley.
Silverman, B. W. (1986). Density Estimation for Statistics and Data Analysis. Chapman & Hall/CRC. London.
Wand, M. P. and Jones, M. C. (1995). Kernel Smoothing. Chapman and Hall, London.
Wolfgang, H. (1991). Smoothing Techniques, With Implementation in S. Springer-Verlag, New York.
plot.kernel.conv
, kernapply
in package "stats"
for computes the convolution between an input sequence, and convolve
use the Fast Fourier Transform (fft
) to compute the several kinds of
convolutions of two sequences.
kernels <- eval(formals(kernel.conv.default)$kernel)
kernels
## gaussian
kernel.conv(x = 0,kernel=kernels[1],deriv.order=0)
kernel.conv(x = 0,kernel=kernels[1],deriv.order=1)
## silverman
kernel.conv(x = 0,kernel=kernels[9],deriv.order=0)
kernel.conv(x = 0,kernel=kernels[9],deriv.order=1)
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