[Numpy-discussion] non-standard standard deviation
Charles R Harris
charlesr.harris@gmail....
Sun Dec 6 10:41:19 CST 2009
On Sun, Dec 6, 2009 at 9:21 AM, <josef.pktd@gmail.com> wrote:
> On Sun, Dec 6, 2009 at 11:01 AM, Colin J. Williams <cjw@ncf.ca> wrote:
> >
>
<snip>
> What's the best estimate? That's the main question
>
> Estimators differ in their (sample or posterior) distribution,
> especially bias and variance.
> Stein estimator dominates OLS in the mean squared error, so although
> it is biased, the variance of the estimator is smaller than OLS so that
> MSE (bias plus variance) is also smaller for Stein estimator than for OLS.
> Depending on the application there could be many possible loss functions,
> including asymmetric, eg. if its more costly to over than to under
> estimate.
>
> The following was a good book for this, that I read a long time ago:
> Statistical decision theory and Bayesian analysis By James O. Berger
>
>
> http://books.google.ca/books?id=oY_x7dE15_AC&pg=PP1&lpg=PP1&dq=berger+decision&source=bl&ots=wzL3ocu5_9&sig=lGm5VevPtnFW570mgeqJklASalU&hl=en&ei=P9cbS5CSCIqllAf-0f3xCQ&sa=X&oi=book_result&ct=result&resnum=4&ved=0CBcQ6AEwAw#v=onepage&q=&f=false
>
>
At last, an explanation I can understand. Thanks Josef.
Chuck
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