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,
I presume that you are also looking for an example that somebody might
actually be tempted to use? Otherwise it's easy; use twice the sample
mean to estimate the population mean!
More seriously, using the sample median as a robust estimator of the
population mean is consistent if the population is symmetric, but
inconsistent in most other cases. It converges to the wrong value as n
-> infinity.
Using the sample mean to estimate the center of a shifted Cauchy
distribution is not consistent.
Neither, for almost any estimator, is randomly selecting a fixed-size
subsample of the data and using that instead of the whole sample.
This,and the last example, do not converge as n -> infinity.
One of the main things that your audience _should_ learn about
consistency is that it is a rather weak condition satisfied by most
real-world statistics.
-Robewrt Dawson
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