HeightMapAlg {bicreduc}R Documentation

HEIGHT MAP ALGORITHM

Description

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

Usage

HeightMapAlg(R,B)

Arguments

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.

Value

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.

Author(s)

Marloes Maathuis: marloes@stat.washington.edu

References

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 http://www.stat.washington.edu/marloes

Examples

# 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                                               

[Package bicreduc version 0.4-7 Index]