awsuni {aws} | R Documentation |
Performes one-dimensional Adaptive Weigths Smoothing (depreciated version, use aws instead)
awsuni(y, lambda=3, gamma=1.3, eta =4, s2hat = NULL, kstar = length(radii), radii = c(1:8,(5:12)*2,(7:12)*4,(7:12)*8,(7:10)*16,(6:8)*32, (5:8)*64,(5:8)*128,(5:8)*256), rmax=max(radii),graph = FALSE,z0 = NULL, eps = 1e-08, control="dyadic", demomode=FALSE)
y |
observed values (ordered by value of independent variable) |
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 vector of same length 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, rmax and eps |
radii |
radii of neighbourhoods used |
rmax |
maximal radius of neighborhood to be used, may change kstar |
graph |
logical, if TRUE progress (for each iteration) is illustrated grahically, if FALSE the program runs until the final estimate is obtained (much faster !!!) |
z0 |
allows for submission of "true" values for illustration and test purposes; only if graph=TRUE, MSE and MAE are reported for each iteration step |
eps |
stop iteration if $||(yhatnew - yhat)||^2 < eps * sum(s2hat)$ |
control |
the control step is performed in either a dyadic sceme ("dyadic") or using all previous estimates (otherwise) |
demomode |
if TRUE the function will wait for user input after each iteration; only if graph=TRUE |
A list with components
yhat |
estimates of the regression function (corresponding to the y's) |
shat |
estimated standard deviations of yhat (conditional on the chosen weights) |
args |
Main arguments supplied to awsuni |
Although the algorithm evaluates a regression model the structure of the regression function only depends on the ordering of the independent variable. Therefore no independent variable is to be given as a parameter but the values of the dependent variable are required to be ordered by the value of the independent variable. This function is superseded by function aws and will be removed in the next mayor version of the package.
Joerg Polzehl polzehl@wias-berlin.de
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
# Blocks data (from Donoho, Johnstone, Kerkyacharian and Picard (1995)) mofx6 <- function(x){ xj <- c(10,13,15,23,25,40,44,65,76,78,81)/100 hj <- c(40,-50,30,-40,50,-42,21,43,-31,21,-42)*.37 Kern <- function(x) (1-sign(x))/2 apply(Kern(outer(xj,x,"-"))*hj,2,sum) } x <- seq(0,1,1/2047) fx6 <- mofx6(x) # sigma==3 y <- rnorm(fx6,fx6,3) tmp <- awsuni(y) par(mfrow=c(1,1)) plot(x,y) lines(x,tmp$yhat,col=2) lines(x,fx6,col=3) title(expression(paste("AWS Reconstruction of blocks data ",sigma==3))) rm(x,y,fx6,mofx6,tmp)