The A matrix is an n by k matrix of zeros and ones, where each row represents one of n failure times,
and each column represents
a possible interval for the nonparametric maximum likelihood estimate (NPMLE).
The function Aintmap creates an A matrix and associated intmap
from left and right intervals (L and R) which may not may not include the boundary
of the interval (using Lin or Rin).
The matrix intmap denotes the intervals of the potential jumps in the distribution of the
NPMLE,
and its attribute LRin denotes whether to include each of the intervals
or not. Called by icfit.
Aintmap(L,R,Lin=NULL,Rin=NULL)A list with two objects:
an n by k matrix of 0 and 1s
the associated intmap
numeric vector of left endpoints of censoring interval
numeric vector of right endpoints of censoring interval
logical vector, should L be included in the interval? (see details)
logical vector, should R be included in the interval? (see details)
The Lin and Rin specify whether or not to include the ends of the intervals.
They may be length 1 (and apply to all n values) or length n. The function automatically
only returns the innermost intervals (also called the Turnbull intervals [see Turnbull, 1976], or the regions of the maximal cliques
[see Gentleman and Vandal, 2002]).
The innermost intervals give the "primary reduction" of Aragon and Eberly (1992).
Aragon, J and Eberly, D (1992). On convergence of convex minorant algorithms for distribution estimation with interval-censored data. J. of Computational and Graphical Statistics. 1: 129-140.
Gentleman R, and Vandal, A (2002). Nonparametric estimation of the bivariate CDF for arbitrarily censored dtaa. Canadian J of Stat 30: 557-571.
Turnbull, B (1976). The empirical distribution function with arbitrarily grouped, censored and truncated data. JRSS-B, 38: 290-295.
Called from icfit and ictest
Aintmap(c(2,3,3,7),c(3,5,5,8),Lin=c(FALSE,TRUE,FALSE,FALSE),Rin=c(TRUE,FALSE,TRUE,FALSE))
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