AWS is a library containing functions to perform
structural adaptive smoothing (adaptive weights smoothing) 
as introduced in 

[1] 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.

[2] Polzehl, J. and Spokoiny, V. (2003). Varying coefficient regression 
modeling by adaptive weights smoothing, WIAS-Preprint 818.

[3] Polzehl, J. and Spokoiny, V. (2002). Local likelihood modelling by 
adaptive  weights smoothing, WIAS-Preprint 787.
     
Revised versions of [2] and [3] are available from


URL: http://www.wias-berlin.de/project-areas/stat/projects/awspapers.html

Changes from version 1.2.0:

- functions aws and laws now carry an additional argument wghts. This allows
  to grow local elliptical neightborhoods instead of circular neighborhoods,
  i.e. to adjust for different distances in the coordinates or different
  influence of explanatory variables.

- additional function   awsh  covers the case of univariate heteroscedastic regression

- several errors in the documentation have been corrected

- some errors have been corrected

Changes from version 1.1.0:

- defaults for parameter lambda have been changed

- some changes in the code to allow for a better memory usage in 3D


Changes from version 1.0.x:

- the license has been changed to GPL version 2 or newer

- the procedures from [1] have been thoroughly revised. The functionality of
  awsbi, awstri and awsuni has been integrated into the new function aws. 
  The three functions are still provided but their use is depreciated. Analog
  results can be obtained using function aws with parameter lkern="Uniform".

- the function aws is based on the procedure introduced in [2]. It is designed 
  for general regression models with additive sub-Gaussian errors. The 
  structural assumption used is that the underlying regression function can be 
  well approximated by a local polynomial model of specified degree. The 
  function provides the following additional functionality:

   - use of a general location kernel 
   
   - use of local polynomial models, arbitrary degree in 1 dimensional 
     problems, up to quadratic models in 2-D problems on a grid, and local 
     linear in 3-D problems on a grid and for a general fixed design.
     
Please see [2] and the help-pages for function aws for details.
   
- the function laws implements the likelihood based approach proposed in [3]. 
The response Y is assumed to be distributed according to a distribution F 
that belongs to a 1-parameter exponential family with parameter theta(x) 
depending on the values of a design variable x. The approach uses the 
structural assumption that the function theta(x) can be locally approximated 
by constant.
Currently the following models are implemented:

    - Poisson-distribution
    
    - Bernoulli-distribution
    
    - Exponential-distribution
    
    - Gaussian-distribution with fixed variance (this coincides with the local 
      constant models in function aws)
            
    - Volatility models (Gaussian distribution with expectation 0 and 
      standard deviation theta)

    - Weibull-distribution
    
- the function awsdens allows for 1D, 2D and 3D density estimation based on 
the assumption that the density can be reasonably approximated by a local 
constant function. This may be of interest mainly in 2D and 3D situations to 
describe the support of the density.
The approach is based on the asymptotic equivalence of density estimation and 
Poisson regression and employs the likelihood approach to Poisson regression 
provided with function laws. See [3] for details.

- the function awstindex provides an estimate of the tail-index of a 
univariate distribution. See again [3] for details.

Joerg Polzehl
email: polzehl@wias-berlin.de
URL: http://www.wias-berlin.de/private/polzehl
