awsuni {aws}R Documentation

One-dimensional Adaptive Weights Smoothing

Description

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

Usage

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)

Arguments

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

Value

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

Note

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 This function is superseded by function aws and will be removed in the next mayor version of the package.

Author(s)

Joerg Polzehl polzehl@wias-berlin.de

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, awstri

Examples

#  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)

[Package aws version 1.3-0 Index]