paws with homogeneous covariance structureThe function implements a vector-valued version the propagation separation approach that
uses patches instead of individuel voxels for comparisons in parameter space. Functionality is analog to function vaws. Using patches allows for an improved
handling of locally smooth functions and in 2D and 3D for improved smoothness of
discontinuities at the expense of increased computing time.
vpaws(y, kstar = 16, sigma2 = 1, mask = NULL, scorr = 0, spmin = 0.25,
ladjust = 1, wghts = NULL, u = NULL, maxni = FALSE, patchsize = 1)
vpawscov(y, kstar = 16, invcov = NULL, mask = NULL, scorr = 0, spmin = 0.25,
ladjust = 1, wghts = NULL, u = NULL, maxni = FALSE, patchsize = 1)y contains the observed response data. dim(y) determines the dimensionality and extend of the grid design. First component varies over components of the response vector.
maximal number of steps to employ. Determines maximal bandwidth.
specifies a homogeneous error variance.
array of voxelwise inverse covariance matrixes, first index corresponds to upper diagonal inverse covariance matrix.
logical mask. All computations are restrikted to design poins within the mask.
The vector scorr allows to specify a first order correlations of the noise for each coordinate direction,
defaults to 0 (no correlation).
determines the form (size of the plateau) in the adaptation kernel. Not to be changed by the user.
factor to increase the default value of lambda
wghts specifies the diagonal elements of a weight matrix to adjust for different distances between grid-points
in different coordinate directions, i.e. allows to define a more appropriate metric in the design space.
a "true" value of the regression function, may be provided to
report risks at each iteration. This can be used to test the propagation condition with u=0
If TRUE use \(max_{l<=k}(N_i^{(l)}\) instead of \((N_i^{(k)}\) in the definition of the statistical penalty.
positive integer defining the size of patches. Number of grid points within the patch is (2*patchsize+1)^d with d denoting the dimensionality of the design.
returns anobject of class aws with slots
y
dim(y)
numeric(0)
integer(0)
logical(0)
Estimates of regression function, length: length(y)
sequence of bandwidths employed
Mean absolute error for each iteration step if u was specified, numeric(0) else
Peak signal-to-noise ratio for each iteration step if u was specified, numeric(0) else
approx. variance of the estimates of the regression function. Please note that this does not reflect variability due to randomness of weights.Currently also uses factor 1/ni instead of the correct
sum(wij^2)/ni^2
numeric(0)
numeric(0)
numeric(0), ratio of distances wghts[-1]/wghts[1]
0
effective hmax
provided or estimated error variance
scorr
family
shape
integer code for lkern, 1="Plateau", 2="Triangle", 3="Quadratic", 4="Cubic", 5="Gaussian"
effective value of lambda
effective value of ladjust
aws
memory
homogen
FALSE
"Constant"
numeric(0)
the arguments of the call to aws
see vaws. The procedure is supposed to produce superior results if the assumption of a local constant image is violated or if smooothness of discontinuities is desired.
Joerg Polzehl, Vladimir Spokoiny, Adaptive Weights Smoothing with applications to image restoration, J. R. Stat. Soc. Ser. B Stat. Methodol. 62 , (2000) , pp. 335--354
Joerg Polzehl, Vladimir Spokoiny, Propagation-separation approach for local likelihood estimation, Probab. Theory Related Fields 135 (3), (2006) , pp. 335--362.
# NOT RUN {
setCores(2)
y <- array(rnorm(4*64^3),c(4,64,64,64))
yhat <- vpaws(y,kstar=20)
# }
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