[SciPy-dev] Statistics Review progress
Robert Kern
robert.kern at gmail.com
Fri Apr 14 02:43:14 EDT 2006
Travis Oliphant wrote:
> Robert Kern wrote:
>>Hmmm. It occurs to me that "bias" or "mean squared error" is probably best
>>defined in the logarithmic space for strictly positive quantities like variance.
>>Then the standard deviation is just a scale away, and the "biasedness" ought to
>>be invariant.
>>
>>This is off-topic, but has anyone seen any publications taking this approach?
>
> I have not seen any, but I think you are spot-on.
Interestingly, when you define the "error" of the variance estimator to be
log(vhat/real_var), the minimum mean squared error estimator in the family
power(x - x.mean(), 2).mean() / y
gives y=n-2 rather than any of the ones proposed in this thread. Even more
interestingly, it is also unbiased!
At least according to my numerical experiments. I haven't made any rigorous
derivations. Surely this must be Jaynes' book somewhere. I'll have to check when
I get back to the office.
--
Robert Kern
robert.kern at gmail.com
"I have come to believe that the whole world is an enigma, a harmless enigma
that is made terrible by our own mad attempt to interpret it as though it had
an underlying truth."
-- Umberto Eco
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