README file:  Interval Censoring Programs

1.  "IntervalCensoring"  is a  C  application written by 
    Piet Groeneboom to implement the methods discussed
    in the book
   
        Groeneboom, P. and Wellner, J. A. (1992)
        Information Bounds and Nonparametric 
        Maximum Likelihood Estimation. 
        Birkhauser, Basel.  
        (go the the URL 
         http://www.stat.washington.edu/jaw/RESEARCH/BOOKS/book2.html
        for more information.
		
		See also Groeneboom, P. (1996)
		Lectures on inverse problems}, in: Lectures on probability  
		theory, Ecole d'Et\'e de Probabilit\'es de Saint-Flour XXIV-1994,
		Editor: P.   Bernard. Springer Verlag, Berlin.
 
2.  The model for "Interval-censored data" treated here means that:
    (a)  X_1 , ... , X_n  are i.i.d. with d.f.  F
    (b)  (U_1, V_1), ... , (U_n, V_n) are i.i.d. pairs with U_i < V_i , 
         which are independent of the X_i's in (a).
    (c)  observations consist of (U_i , V_i , D_i  ), i = 1, ... , n 
         where
            D_i =  1     if  X_i <= U_i ,            
            D_i =  2     if  U_i < X_i <= V_i ,  
            D_i =  3	 if  V_i < X_i .
     
     The object is to estimate the unknown d.f. F  nonparametrically;
     the estimator computed in the program is the NPMLE (nonparametric 
     maximum likelihood estimator).

2.  Methods available in the program:
        ICM algorithm; the iterative convex minorant algorithm as 
                 described in Groeneboom and Wellner (1992);
        EM algorithm;
        Hybrid algorithm (alternating steps of EM and ICM),
        or Iterative Convex Minorant).
        One can choose to do ICM, EM, or Hybrid in the menu
        "Algorithms". The default is set on the Hybrid algorithm.
        One can also switch between the two by the keyboard equivalents
        "command-1" and "command-2".
            
3.  Data included and generated in the application:

     (i)	the data sets of size n = 100, 1000 called
        	data100, and data1000, respectively, generated from a
		  	Uniform(0,1) distribution for the X_i and the Uniform
			distribution for (U_i,V_i) on the upper triangle of the unit
			square. This situation is analyzed in detail, in particular in
			connection with smooth functional estiamtion, in Groeneboom (1996).
     (ii)	Monte-Carlo generation routines for the
         	situation where the X_i are generated by a standard exponential
			distribution, and the (U_i,V_i) are the order statistics of a
			sample of size 2 from a standard exponential distribution. 
   
     One can choose to use input files or to generate random samples
     by the menu "Samples".

4.  User-specified data is allowed; input files should be in 
    the form of three columns, the first two for U_i,V_i, 
    and the third for the indicators D_i;
    see the format of the example files data100, and data1000.
    
5.  For running one of the algorithms on either input files or randomly
	generated data, press "command-r" or use the menu "Run".

6.  Output: 
      (i) values of the Fenchel conditions and log-likelihood for successive
          iterations of the algorithm. For more information on the Fenchel
          conditions, see the reference above: Groeneboom and Wellner (1992).
          The iterations can be stopped at any time (particularly needed
          for the EM algorithm) by pressing "command-period" (="apple-period").
          The iterations are stopped automatically if the criteria are zero in
          6 decimals. The text output of the iterations can be saved if desired,
          the name can be specified in the dialog box that will appear.
		  The value of the estimator at the end of the iterations
          is written to a file called "NPMLE" giving the NPMLE at the 
          jump times (not at all observations).
      (ii) a plot of the estimated d.f.  F, which can be saved as a PICT
           file via the menu or "command-s". The PICT file can be opened
           by SimpleText or applications like Adobe Illustrator or Mathematica.
           One can exit the plot by pressing return or clicking the 
           "go-away" box.
      
      Because the output files are large for big n, usually bigger 
      than 32K, the program uses a freeware replacement of the Apple
      toolbox Text Edit routines. At the time that the program was written
      (1996), the toolbox Text Edit routines still had the limitation of 32K.
      Since in Mac OS 8.1 SimpleText still refuses to open files bigger 
      than 32K, we fear that the situation in this respect still has not changed,
      which is an absolute disgrace in this day and age!
      The replacement of the Apple toolbox Text Edit routines is called 
      TE32K.c and was written by Roy Wood and Michael J. Lowe, whose 
      contribution (given unknowingly) is gratefully acknowledged. 
      The text files that are produced can be read by any editor that 
      can handle text files bigger than 32K
      (in which case they cannot be read by SimpleText!), like 
      BBEdit or Textures.
          
7.  For more information on Macintosh compatible 
    C source code for this program, please contact
    either Jon Wellner or Piet Groeneboom.  
    (Copyright issues are involved in making source code available.)

Written by Jon Wellner and Piet Groeneboom,  June 1998.