Constraints are a common feature of statistical models. CML is a
computer program designed to produce estimates efficiently for these
kinds of models.
Methods of statistical inference for these models is more
difficult, however. When confidence limits of all parameters
n a model are more than 
,
standard methods will apply and the constraints will have
no implications for inference. However, when this does
not pertain, the constraint boundaries may affect
the inference.
When the only parameter in the model within 
of a
constraint boundary is the parameter of interest, inversion of
a mixture of chi-square statistics will be required. A correction
for this case is incorporated into CML.
When one (or more) nuisance parameter is within
of a constraint boundary is correlated by more than about
.7 with the parameter of interest, whether or not the parameter
of interest is itself
near a constraint boundary - the chi-square statistics have
complex distributions. While methods exist for determining the
properties of their distributions when the true values are on the
boundaries, there is no known method for determining them
when the true values are only near the boundaries.
It is clear from the Monte Carlo evidence that effects near boundaries overwhelm these effects on the boundary, rendering any standard inference in these circumstances quite hazardous.