vaws {aws}  R Documentation 
aws
The function implements the propagation separation approach to
nonparametric smoothing (formerly introduced as Adaptive weights smoothing)
for varying coefficient likelihood models with vector valued response on a 1D, 2D or 3D grid.
The function implements a version the propagation separation approach that uses vector valued instead of scalar responses.
vaws(y, kstar = 16, sigma2 = 1, mask = NULL, scorr = 0, spmin = 0.25, ladjust = 1, wghts = NULL, u = NULL, maxni = FALSE) vawscov(y, kstar = 16, invcov = NULL, mask = NULL, scorr = 0, spmin = 0.25, ladjust = 1, wghts = NULL, u = NULL, maxni = FALSE)
y 

kstar 
maximal number of steps to employ. Determines maximal bandwidth. 
sigma2 
specifies a homogeneous error variance. 
invcov 
array of voxelwise inverse covariance matrixes, first index corresponds to upper diagonal inverse covariance matrix. 
mask 
logical mask. All computations are restrikted to design poins within the mask. 
scorr 
The vector 
spmin 
determines the form (size of the plateau) in the adaptation kernel. Not to be changed by the user. 
ladjust 
factor to increase the default value of lambda 
wghts 

u 
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 
maxni 
If TRUE use max_{l<=k}(N_i^{(l)} instead of (N_i^{(k)} in the definition of the statistical penalty. 
see aws
. Expets vector valued responses. Currently only implements the case of additive Gaussian errors.
returns anobject of class aws
with slots
y = "numeric" 
y 
dy = "numeric" 
dim(y) 
x = "numeric" 
numeric(0) 
ni = "integer" 
integer(0) 
mask = "logical" 
logical(0) 
theta = "numeric" 
Estimates of regression function, 
hseq = "numeric" 
sequence of bandwidths employed 
mae = "numeric" 
Mean absolute error for each iteration step if u was specified, numeric(0) else 
psnr = "numeric" 
Peak signaltonoise ratio for each iteration step if u was specified, numeric(0) else 
var = "numeric" 
approx. variance of the estimates of the regression function. Please note that this does not reflect variability due to randomness of weights. 
xmin = "numeric" 
numeric(0) 
xmax = "numeric" 
numeric(0) 
wghts = "numeric" 
numeric(0), ratio of distances 
degree = "integer" 
0 
hmax = "numeric" 
effective hmax 
sigma2 = "numeric" 
provided or estimated (inverse) error variance 
scorr = "numeric" 
scorr 
family = "character" 
family 
shape = "numeric" 
shape 
lkern = "integer" 
integer code for lkern, 1="Plateau", 2="Triangle", 3="Quadratic", 4="Cubic", 5="Gaussian" 
lambda = "numeric" 
effective value of lambda 
ladjust = "numeric" 
effective value of ladjust 
aws = "logical" 
aws 
memory = "logical" 
memory 
homogen = "logical" 
homogen 
earlystop = "logical" 
FALSE 
varmodel = "character" 
"Constant" 
vcoef = "numeric" 
numeric(0) 
call = "function" 
the arguments of the call to 
use setCores='number of threads'
to enable parallel execution.
Joerg Polzehl, polzehl@wiasberlin.de, http://www.wiasberlin.de/people/polzehl/
J. Polzehl, K. Tabelow (2019). Magnetic Resonance Brain Imaging: Modeling and Data Analysis Using R. Springer, Use R! series. Appendix A. Doi:10.1007/9783030291846.
J. Polzehl, V. Spokoiny, Adaptive Weights Smoothing with applications to image restoration, J. R. Stat. Soc. Ser. B Stat. Methodol. 62 , (2000) , pp. 335–354. DOI:10.1111/14679868.00235.
J. Polzehl, V. Spokoiny, Propagationseparation approach for local likelihood estimation, Probab. Theory Related Fields 135 (3), (2006) , pp. 335–362. DOI:10.1007/s0044000504641.
See also aws
, vpaws
,link{awsdata}
## Not run: setCores(2) y < array(rnorm(4*64^3),c(4,64,64,64)) yhat < vaws(y,kstar=20) ## End(Not run)