here is the simplest example of inconsistent statistcs you can imagine:
let X1, X2, ..., Xn be a sample of iid random variables with mean M.
lets consider the following statistic t for M:
t=x1
it's clearly inconsistent because it does not change at all as n grows.
(and of course it`s unbiased stat)
I think any audience can get it :)
On Wed, 6 Sep 2000, Chuck Cleland wrote:
> Hello:
> If I understand the concept correctly, a consistent statistic is one
> whose value approaches the population value as the sample size
> increases. I am looking for examples of statistics that are _not_
> consistent. The best examples would be statistics that are not
> computationally complex and could be understood by large and diverse
> audiences. Also, how can one go about demonstrating the statistic is
> not consistent thru simulation?
>
> thanks for any suggestions,
>
> Chuck
>
> O~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~O
> | |
> | Chuck Cleland |
> | Institute for the Study of Child Development |
> | UMDNJ--Rober Wood Johnson Medical School |
> | 97 Paterson Street |
> | New Brunswick, NJ 08903 |
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> | fax: (732) 235-6189 |
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> 0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~O
>
>
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