Description Usage Arguments Details Value Author(s) References See Also Examples
The (S3) generic function kernel.conv
computes the convolution
of r'th derivative for kernel function.
1 2 3 4 5 | 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(x;r)*K(x;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(x;r)*k(x;r) = int K(y;r) K(x-y;r) dy
where:
K(x;r) = d^r / dx^r K(x)
for r = 0, 1, 2, …
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.
1 2 3 4 5 6 7 8 9 10 | 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)
|
[1] "gaussian" "epanechnikov" "uniform" "triangular" "triweight"
[6] "tricube" "biweight" "cosine" "silverman"
$kernel
[1] "gaussian"
$deriv.order
[1] 0
$x
[1] 0
$kx
[1] 0.2820948
attr(,"class")
[1] "kernel.conv"
$kernel
[1] "gaussian"
$deriv.order
[1] 1
$x
[1] 0
$kx
[1] -0.1410474
attr(,"class")
[1] "kernel.conv"
$kernel
[1] "silverman"
$deriv.order
[1] 0
$x
[1] 0
$kx
[1] 0.265165
attr(,"class")
[1] "kernel.conv"
$kernel
[1] "silverman"
$deriv.order
[1] 1
$x
[1] 0
$kx
[1] -0.08838835
attr(,"class")
[1] "kernel.conv"
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