README file:  Estimation of a k-monotone density via maximum 
              likelihood and least squares together with computation 
              of (approximations) to the maximum likelihood = LS 
              estimator in the canonical form of the limit Gaussian
              problem
              

1.  These C-programs were developed by Fadoua Balabdaoui starting from 
    C-programs and MatLab programs for the case k=2 
    written by Piet Groeneboom and Geurt Jongbloed at Delft University 
    and the Vrije Universiteit Amsterdam.  These programs were used, 
    in particular to carry out the calculations in
    
       Balabdaoui, F. and Wellner, J. A. (2004b). 
       Estimation of a k-monotone density, part 2:
       algorithms for computation and numerical results.
       Technical Report No. 460, Department of Statistics, University 
       of Washington.

    We are very grateful to Piet Groeneboom and Geurt Jongbloed
    for sharing their programs for the case k=2 with us.  
    Fadoua has modified their programs and recast them in S.  
    We take full responsibility for any errors resulting
    from the changes made.  Fadoua Balabdaoui is very grateful to Karim Filali,
    Department of Computer Science, for translating her S programs for generating
    multiply integrated Brownian motion into C.

2.  Steps for producing estimators from data:

     To produce either the ML or LS estimators in  Splus, 
     one needs to follow only two steps:

     A- Type 'library(matrix)' in the commands window/a script file: 
     this will download the library 'Matrix' which contains functions 
     that are able to invert bad-conditioned matrices.

     B- After specifying the arguments, type 

            ' SuppReducAlgoMLE (K=, X=, prec=...)'
   
     in the commands window/a script file to compute the MLE or
    
              'LSESupReducAlgo(K=, X=, prec=...)' to compute the LSE.
              
              
              
Written by Fadoua Balabdaoui and Jon Wellner, November 2004.