aws (version 1.3-3.1)

awstri: Three-dimensional Adaptive Weights Smoothing

Description

Performes three-dimensional Adaptive Weigths Smoothing (depreciated version, use aws instead)

Usage

awstri(y, lambda=3, gamma=1.3, eta =4, s2hat = NULL, kstar = length(radii),
       rmax=max(radii), weight = c(1,1,1), radii = c((1:4)/2,2.3,(5:12)/2,7:9,10.5,12,13.5), control="dyadic")

Arguments

y

array of observed values

lambda

main smoothing parameter (should be approximately 3)

gamma

allow for increase of variances during iteration by factor gamma (!!gamma >=1)

eta

main control parameter (should be approximately 4)

s2hat

initial variance estimate (if available, can be either a number (homogeneous case), a matrix of same dimension as y (inhomogeneous variance) or NULL (a homogeneous variance estimate will be generated in this case)

kstar

maximal number of iterations to perform, actual number may be smaller depending on parameters radii and rmax

weight

weights used for distances, determining elliptical neighborhoods

radii

radii of circular neighbourhoods used

rmax

maximal radius of neighborhood to be used, may change kstar

control

the control step is performed in either a dyadic sceme ("dyadic") or using all previous estimates (otherwise)

Value

• A list with components
• yhat
  estimates of the regression function (matrix corresponding to the y's)
• shat
  estimated standard deviations of yhat (conditional on the chosen weights)
• args
  Main arguments supplied to awstri

References

Polzehl, J. and Spokoiny, V. (2000). Adaptive Weights Smoothing with applications to image restoration, J.R.Statist.Soc. B, 62, Part 2, pp.335-354

See Also

aws, awsbi,awsuni

Examples

xy <- rbind(rep(0:30,31),rep(0:30,rep(31,31)))
w3 <- array(0,c(31,31,31))
w3[4:28,4:28,4:28] <- 1
dim(w3) <- c(961,31)
w3[((xy[1,]-15)^2+(xy[2,]-15)^2)<=144,16] <- 0
for(i in 1:12) {
   r2 <- 144-i*i
   w3[((xy[1,]-15)^2+(xy[2,]-15)^2)<=r2,16+c(-i,i)] <- 0
}
dim(w3) <- c(31,31,31)
w3[10:22,10:22,10:22] <- 1
dim(w3) <- c(961,31)
w3[((xy[1,]-15)^2+(xy[2,]-15)^2)<=36,16] <- 0
for(i in 1:6) {
   r2 <- 36-i*i
   w3[((xy[1,]-15)^2+(xy[2,]-15)^2)<=r2,16+c(-i,i)] <- 0
}
dim(w3) <- c(31,31,31)
sigma <- .4
y <- w3+rnorm(w3,0,sigma)
#  increase rmax for better results
yhat <- awstri(y,rmax=2)
rm(y,yhat,w3,xy)