FAQ.txt
Some of the FAQ.
Q1. The function el.cen.EM2( ) sometimes do not give a regular result
and stop computing.
A1.
Short answer: the constraints/hypothesis must be feasible.
If multiple constraints are involved, they must be compatible
and non-redundant.
Longer answer: This is often due to the fact that: the constrain(s) given,
or the hypothesis been tested is/are too extreme or impossible.
For example, if the g( ) function is always non-negative, but the
hypothesis to be tested is "the mean of g equals -2".
[this is called non-feasible]
This is impossible, and therefore there is no CDF satisfy this hypothesis.
The search for CDF that satisfy this requiement will stop
and produce nothing.
Another possibility is when you have several constraints,
they may be contradictory to one other, i.e. a CDF satisfy the
first constraint cannot
satisfy the second at the same time. etc. in this case the
computation will stop.
So constraints must be compatible to each other.
We can either treat those "no result, stop computation" case as p-value 0
(since it is impossible) or change the hypothesis.
This problem some time happens in the simulation runs: in 100 runs
only 3 had problems. This is because the samples are random, and for
some samples, there exist a tilted empirical CDF that satisfy the
hypothesis, yet for other samples, there may be no tilted empirical
CDF that satisfy the hypothesis. (remember our search of max is
limited to those that are "absolutely
continuous" wrt the empirical CDF, or tilting.
These case usually happen more often for smaller samples, since the
extend of possible tilting (probability has to be between 0 and 1)
produces limited change in mean value
for smaller samples. For larger samples, a small tilting can result
in a larger change in the mean value, therefore it usually covers
more "feasible values"