[EMAIL PROTECTED] (Jason Owen) wrote in message news:<[EMAIL PROTECTED]>...
> Hello,
>
> Does anyone know of references for limit theorems
> involving xbar where the convergence rate is something
> other than sqrt(n)? What I'm thinking of is cases where
> the Xi's are not independent -- so that the conditions of
> the CLT are not satisfied -- but asymptotic normality is
> still achieved for a different power of n.
>
> Thanks in advance -- please post suggestions to this
> newsgroup.
>
> Jason
If the Xi's are independent, but not identically distributed, you can
sometimes converge to a normal with convergence rate
sqrt{sum_1^n{var{Xi}} (see Jacod and Protter). If the Xi's are iid but
without finite variance, you can sometimes converge to a (not
necessarily normal) stable law with rate other than sqrt{n} (see
Durrett). If you want the Xi's dependent, it's harder to find results.
One nice result is the martingale CLT; there the Xi's can be
dependent, but the rate is sqrt{n} (see Jacod and Protter). There's
also a concept of m-dependence, for which there are CLTs, though I
don't have an immediate reference.
.
.
=================================================================
Instructions for joining and leaving this list, remarks about the
problem of INAPPROPRIATE MESSAGES, and archives are available at:
. http://jse.stat.ncsu.edu/ .
=================================================================
