PGM: An implementation of the projected gradient methods for finding the NPMLE.

Description

An estimate of the NPMLE is obtained by using projected gradient methods. This method is a special case of the methods described in Wu (1978).

Usage

PGM(A, pvec, maxiter = 500, tol=1e-07, told=2e-05, tolbis=1e-08, keepiter=FALSE)

Arguments

A is either the m by n clique matrix or the n by 2 matrix containing the left and right end points for each event time.

pvec

An initial estimate of the probability vector.

maxiter

The maximum number of iterations to take.

tol

The tolerance for decreases in likelihood.

told

told does not seem to be used.

tolbis

The tolerance used in the bisection code.

keepiter

A boolean indicating whether to return the number of iterations.

Value

pf: The NPMLE of pvec.
sigma: The cumulative sum of pvec.
lval: The value of the log likelihood at pvec.
clmat: The clique matrix.
method: The method used, currently only "MPGM" is possible.
lastchange: The difference between pf and the previous iterate.
numiter: The number of iterations carried out.
eps: The tolerances used.
converge: A boolean indicating whether convergence occurred within maxiter iterations.
iter: If keepiter is true then this is a matrix containing all iterations - useful for debugging.

Details

New directions are selected by the projected gradient method. The new optimal pvec is obtained using the bisection algorithm, moving in the selected direction. Convergence requires both the $L_1$ distance for the improved pvec and the change in likelihood to be below tol.

References

Some Algorithmic Aspects of the Theory of Optimal Designs, C.--F. Wu, 1978, Annals.

Examples

Run this code

    data(cosmesis)
    csub1 <- subset(cosmesis, subset=Trt==0, select=c(L,R))
    PGM(csub1)
    data(pruitt)
    PGM(pruitt)

Run the code above in your browser using DataLab