HeightMapAlg            package:bicreduc            R Documentation

_H_E_I_G_H_T _M_A_P _A_L_G_O_R_I_T_H_M

_D_e_s_c_r_i_p_t_i_o_n:

     The HeightMapAlgorithm computes the regions of possible mass
     support for the NPMLE for the distribution function of bivariate
     interval-censored data.

_U_s_a_g_e:

     HeightMapAlg(R,B)

_A_r_g_u_m_e_n_t_s:

       R: An n x 4 real matrix of n observation rectangles. Each row
          corresponds to an observation rectangle, represented as
          (x1,x2,y1,y2). Here (x1,y1) is the lower left corner of the
          rectangle and (x2,y2) is the upper right corner of the
          rectangle. We call (x1,x2) the x-interval and (y1,y2) the
          y-interval of the observation rectangle. 

       B: B describes the boundaries of the observation rectangles
          (0=open or 1=closed). It can be specified in three ways:

          (1) An n x 4 matrix containing 0's and 1's. Each row
          corresponds to an observation rectangle, and is denoted as
          (cx1, cx2, cy1, cy2). Here cx1 denotes the boundary type of
          x1, cx2 denotes the boundary type of x2, etc. 

          (2) A vector (cx1, cx2, cy1, cy2) containing 0's and 1's.
          This representation can be used if all rectangles have the
          same type of boundaries. 

          (3) A vector (c1, c2) containing 0's and 1's. This
          representation can be used if all x- and y-intervals have the
          same type of boundaries. c1 denotes the boundary type of x1
          and y1, and c2 denotes the boundary type of  x2 and y2. 

_V_a_l_u_e:

     The function returns an m x 4 matrix, containing the maximal
     intersections, that is the areas where the observation rectangles
     have maximal overlap and where the NPMLE can possibly assign mass.
     Each row (x1,x2,y1,y2) corresponds to a maximal intersection.

_A_u_t_h_o_r(_s):

     Marloes Maathuis: marloes@stat.washington.edu

_R_e_f_e_r_e_n_c_e_s:

     M.H. Maathuis (2005), "Reduction algorithm for the NPMLE for the
     distribution function of bivariate interval-censored data",
     Journal of Computational and Graphical Statistics (to appear). See
     also <URL: http://www.stat.washington.edu/marloes>

_S_e_e _A_l_s_o:

_E_x_a_m_p_l_e_s:

     # an example with 6 arbitrarily chosen observation rectangles
     R1<-c(1.5, 6.2, 7, Inf)         # first rectangle
     R2<-c(2.3, 5, 5.1, Inf)         # second rectangle
     R3<-c(3.8, 9.4, 8.3, 10)        # etc...
     R4<-c(4.1, Inf, 4.2, 6.7)
     R5<-c(7.2, 8.8, 2.7, 9.3)
     R6<-c(10, Inf, 1.1, 3.9)
     R<-rbind(R1,R2,R3,R4,R5,R6)     # R contains all observation rectangles 
     A<-HeightMapAlg(R, c(0,1))      # A contains the maximal intersections
     A                                               

