A good example in regression is when one of the independent (explanatory)
variables is measured with error. For example, suppose the true relation is
y = xb+e
where the estimated relation is
y = x*b + e
and
x* = x + v
where v represents random measurement error. Then the least squres estimate
of b using the mismeasured data x* is biased and inconsistent.
"Robert J. MacG. Dawson" <[EMAIL PROTECTED]> wrote in message
[EMAIL PROTECTED]">news:[EMAIL PROTECTED]...
>
>
> 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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