Description Usage Arguments Details Value Note Author(s) See Also
View source: R/PointProcessKernel.R
The function ppKernel
fits a generalized linear point process model
based on expansions of smooth terms in a reproducing kernel Hilbert space.
1 2 3 | ppKernel(formula, data, family, support = 1, N = 200, Delta, lambda,
coefficients, modelMatrix = TRUE, fit = modelMatrix, varMethod = 'Fisher',
kernel = sobolevKernel, specThres = 1e-8, ...)
|
formula |
an object of class |
data |
an object of class |
family |
an object of class
|
support |
a |
N |
a |
Delta |
a |
lambda |
a |
coefficients |
an optional specification of the parameters. |
modelMatrix |
a |
fit |
a |
varMethod |
a |
kernel |
a |
specThres |
a |
... |
additional parameters that are passed on to
|
ppKernel
preprocesses the formula, and all terms of the form k(.)
are
treated specially as kernel terms when a PointProcessKernel
is created.
Other terms are treated as in a direct call of pointProcessModel
. The kernel
terms are penalized by the norm in the reproducing kernel Hilbert space given by the
kernel.
Using the default kernel, the sobolevKernel
, the resulting fit is almost
identical to that obtained by ppSmooth
. The gaussianKernel
is
available as an alternative. All kernels are called with an additional argument
t = support[2]
, which for the two kernels mentioned rescales the support to
[0,1]. Hence a kernel should allow for such an argument even if it is
ignored.
The kernel enters only through a Gram matrix computation on an N
by N
grid, which is then factorized. The current factorization is via the spectral
decomposition, and for computational efficiency an incomplete factorization is
used. The specThres
argument is the threshold for the smallest eigenvalue
used relative to the largest eigenvalue.
The sandwich estimator depends on the amount of penalization. If the fit is oversmoothed, and thus biased, the resulting confidence intervals on the filter functions are most likely misleading.
The ppKernel
generally requires less memory than ppSmooth
but
gradient computations and thus the estimation can be slower.
An object of class PointProcessKernel
, which is an extension of the
PointProcessModel
class.
The method does not yet support automatic data adaptive selection of lambda
.
An information quantity (which in this case is TIC) can be extracted
using getInformation
. This quantity can be minimized over at grid for selection
of lambda
.
The current implementation is entirely in R. Certain precomputations in ppSmooth
are implemented much more efficiently in compiled code. In future versions the
corresponding precomputations for ppKernel
will be transferred to compiled
code.
Niels Richard Hansen Niels.R.Hansen@math.ku.dk.
PointProcessKernel
, pointProcessModel
, ppSmooth
.
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