n this section we obtain a low bound for variance of an estimator under some
reasonable regularity assumptions.
We use the Cauchy
inequality
where the
is a joint distribution of the sample
We wish to apply the above relationship with
and
hence, we
set
and
We
obtain
Therefore,
The last result is called the CramerRao low bound.
If the variables
are iid then
and the denominator may be
simplified
Hence,
Therefore, according to the last section the MLE asymptotically achieves the
low bound.
