[SciPy-dev] Statistics Review progress

Robert Kern robert.kern at gmail.com
Wed Apr 12 17:42:10 CDT 2006

Stephan Tolksdorf wrote:
> Robert Kern wrote:
>>* We really need to sort out the issue of biased and unbiased estimators. At
>>least, a number of scipy.stats functions compute values that could be computed
>>in two different ways, conventionally given labels "biased" and "unbiased". Now
>>while there is some disagreement as to which is better (you get to guess which I
>>prefer), I think we should offer both.
> I'd like to note that the square root of the unbiased variance estimator
> is not an unbiased estimator of the standard deviation* (see Jensen's
> inequality), which is why unbiasedness is not a terribly useful concept
> in this context.

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?

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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