Hi all,

In statistical modelling of an insurance problem, I wanted to model
the relation between the some premium and the death incidents in a
sample pool, consisting of say, 100, subjects.

The model has a Poisson process as one of its component. Now we are
looking at the problem of estimation the parameters of this model.

The problem is that there is no death event in our data sample. Does
that render the Poisson component of the model unidentifiable?

I guess this is also a model-comparison problem -- with no event of
death, can I distinguish between a model with the counting(Poisson)
component vs. a model with no counting (Poisson) component? Does the
information about "no death or no counts" is itself some information
for identifying the counting model?

On Fri, 18 Apr 2008 13:30:10 -0700 (PDT), Luna Moon

lunamoonm...@gmail.com> wrote:
Hi all,

In statistical modelling of an insurance problem, I wanted to model
the relation between the some premium and the death incidents in a
sample pool, consisting of say, 100, subjects.

The model has a Poisson process as one of its component. Now we are
looking at the problem of estimation the parameters of this model.

The problem is that there is no death event in our data sample. Does
that render the Poisson component of the model unidentifiable?

I suppose someone might apply the term "unidentifiable" but
that seems too weak.

When all the responses on a dichotomy are on one side,
you have "no information" for the purpose of most statistical
tests.



I guess this is also a model-comparison problem -- with no event of
death, can I distinguish between a model with the counting(Poisson)
component vs. a model with no counting (Poisson) component? Does the
information about "no death or no counts" is itself some information
for identifying the counting model?

Statistically, you can model a rate as "low" and discard any
hypothesis that requires a higher rate. But this looks like an
experiment that failed to show anything, for lack of power.

--
Rich Ulrich

http://www.pitt.edu/~wpilib/index.html

On Apr 19, 7:06 pm, Richard Ulrich <Rich.Ulr...@comcast.net> wrote:
On Fri, 18 Apr 2008 13:30:10 -0700 (PDT), Luna Moon

lunamoonm...@gmail.com> wrote:
Hi all,

In statistical modelling of an insurance problem, I wanted to model
the relation between the some premium and the death incidents in a
sample pool, consisting of say, 100, subjects.

The model has a Poisson process as one of its component. Now we are
looking at the problem of estimation the parameters of this model.

The problem is that there is no death event in our data sample. Does
that render the Poisson component of the model unidentifiable?

I suppose someone might apply the term "unidentifiable" but
that seems too weak.

When all the responses on a dichotomy are on one side,
you have "no information" for the purpose of most statistical
tests.



I guess this is also a model-comparison problem -- with no event of
death, can I distinguish between a model with the counting(Poisson)
component vs. a model with no counting (Poisson) component? Does the
information about "no death or no counts" is itself some information
for identifying the counting model?

Statistically, you can model a rate as "low" and discard any
hypothesis that requires a higher rate. But this looks like an
experiment that failed to show anything, for lack of power.

--
Rich Ulrich

http://www.pitt.edu/~wpilib/index.html

Thanks Rich.

What's the overall conclusion?

So there is no way to back out meaningful parameter estimates when all
the responses on a dichotomy are on one side? So the experiment is a
poor one, am I right?

However, if the estimation of this Poisson counting component is
embedded in a joint (bigger) estimation over several pieces all
together, will this piece of "no-information" help the identification
of other components and other components' "information" help the
identification of this Poisson component?

Could you point me to some books and notes talking about this lack of
power due to one sided response problem in statistical experiments? I
need to show to my colleagues...

On Fri, 18 Apr 2008 13:30:10 -0700 (PDT), Luna Moon
lunamoonmoon@gmail.com> wrote:

The problem is that there is no death event in our data sample. Does
that render the Poisson component of the model unidentifiable?

When all the responses on a dichotomy are on one side,
you have "no information" for the purpose of most statistical
tests.