Jason wrote:
> [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.
You might like to seek out references to fractionally differenced
time-series models. Some simple cases of these give results where the
rate of convergence is slower than the "usual result. Hosking is one
author in that area.
David Jones
.
.
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