e approximate
with
where
is the standard normal variable. Suppose the
is drawn as a function of some uniformly distributed on
variable :
.
We
consider
as an alternative procedure for simulation of
.
The
is an unbiased
estimator:
and the convergence in distribution is
We want to compare
with
.
This is a valid comparison if it costs nothing to generate
in addition to
.
We
have
Hence, it suffices to
have
to improve efficiency of simulation.
