
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. If not, the computing will stop.

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(X) 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 etc. 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".
 

 
