[SciPy-dev] Statistics Review progress

[Travis Oliphant]

Robert Kern wrote:

>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?
>  
>

I have not seen any,  but I think you are spot-on.  

-Travis