These are internal functions called by various other functions in the package emplikCS.
They are R codes of Sequential Quadratic Programing to compute the (various) constrained NPMLE
of \(\hat F_n(t)\) with current status data. They all call solve.QP( ) from quadprog package.
They are not intended to be called directly by ordinary users.
CSQP(Itime, d, w0, error=1e-11, maxit=25)
CSQPprob(Itime, d, w0, t0=0.50, Ft0=0.5, error=1e-11, maxit=25)
CSQP2prob(Itime, d, w0, t01=0.4, Ft01=0.4, t02=0.6, Ft02=0.6, error=1e-11, maxit=25)
CSQPmean(Itime,d,w0=rep(.5,length(d)),MU,dp=rep(1,length(d)),error=1e-11,maxit=25)
CSQPmean2(Itime,d,w0=rep(.5,length(d)),MU,dp=rep(1,length(d)),error=1e-11,maxit=25)CSQP( ) calculate the NPMLE of \( \hat F_n(t) \) by using the SQP method to maximize the
empirical likelihood function subject to monotonicity. This should give the same result as PAVA algorithm
provided by isotNEW2( ) in this package. Should also be the same as ComputeMLE( )
from csci package (from slope of GCM algorithm?). We did some tests and all are equal, but
may be more tests are due.
This function is slower than isotNEW2( ), therefore not used often,
other than to proof the SQP algorithm works.
CSQPprob( ) similar to function CSQP( ), but with an extra constraint of F(t0) = Ft0.
The SQP can easily add one equality constraint in addition to the n-1 monotone inequality constraints.
The PAVA and slope of GCM algorithm may also add a constraint, but SQP seem the easiest to do.
CSQP2prob( ) similar to CSQPprob( ) but with two constraints. We may write one for three
constraints similarly.
CSQPmean( ) similar to CSQPprob but the constraint is in terms of the mean
(or a linear functional) of the CDF F(t). The PAVA and slope of GCM algorithm seems not usable here.
CSQPmean2( ) similar to CSQPmean( ).