In article <9adcnm$l9s$[EMAIL PROTECTED]>,
Jason Owen <[EMAIL PROTECTED]> wrote:
>Hello -- I need to know if such a theorem exists.
>Suppose I have a sequence of RVs: X1, X2, ...
>each with mean mu and finite second momment.
>Now, I know that I have asymptotic normality of
>the standardized sample mean if the RVs are independent.
>The rate of the convergence is SQRT(n).
To get this rate of convergence generally requires
a third moment.
>What I want to know is: is there a theorem that states
>asymptotic normality for the standardized mean at a
>rate n^b for some b? In particular, does it allow for a
>relaxing of the independence assumption? For example,
>if there was a dependence within the sequence, perhaps asymptotic
>normality be achieved with an n^(3/4) rate.
>Any thoughts or references are appreciated.
One would have to be very lucky to get rates better
than sqrt(n), or better written, 1/sqrt(n).
The more common case would be to get a worse rate.
Some of the proofs for strong mixing processes, or
stronger, can be used to get rates from the mixing
speed. If the mixing is exponential, I would be
surprised if the rate is not the same as in the
independent case, except for a constant.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
=================================================================
Instructions for joining and leaving this list and remarks about
the problem of INAPPROPRIATE MESSAGES are available at
http://jse.stat.ncsu.edu/
=================================================================
