Stat 804
Lecture 12 Notes
Large Sample Theory for Conditional Likelihood:
We have data X=(Y,Z) and study the conditional likelihood, score
Fisher information and mle:
,
,
and
.
In general standard maximum likelihood theory may
be expected to apply to these conditional objects:
- 1.
-
as the
``sample size'' (often measured by the Fisher information)
tends to infinity.
- 2.
-
- 3.
-
is consistent (converges to the true value as
the Fisher information converges to infinity).
- 4.
- The usual Bartlett identities hold. For example:
- 5.
- The error in the mle has approximately the form
- 6.
- The mle is approximately normal:
(where I is the identity matrix).
- 7.
- The conditional Fisher information can be estimated by the observed information:
- 8.
- The log-likelihood ratio is approximately :
In the previous lecture I showed you 2) and 4) in this list.
Today we look at 5), 6) and 7) in the context of the AR(1)
model
.
Richard Lockhart
1999-11-01