[SciPy-dev] Statistics Review progress

Jonathan Taylor jonathan.taylor at stanford.edu
Fri Apr 14 13:47:23 CDT 2006

the discussion of bias vs. unbiasedness depends on the degrees of 
freedom in the "residuals" (and whether you are estimating the variance 
(sigma^2) or the standard deviation (sigma)).

most (mathematical) stats books refer to unbiased estimates of sigma^2 
as compared to the MLE estimate of sigma^2 (which has denominator n).

so, i think an integer flag something along the lines of "df=n-1" makes 
a lot of sense because
that way, when estimating other standard errors (say the error from a 
linear regression model), the flag would be the same and could be set 
appropriately for these residuals.

just my $0.02

-- jonathan

Ed Schofield wrote:
> Travis Oliphant wrote:
>> How about making the default minimize mean square error  --- i.e  
>> division by N+1 for variance calculation  :-) 
> Robert Kern wrote:
>> I would implement varbiased() and var()
>> def varbiased(a):
>>   return var_with_flag(a, bias=True)
>> def var(a):
>>   return var_with_flag(a, bias=False)
>> I *don't* want three versions of each of these functions.
> If we really want just one version for the three cases with denominators
> (n-1), n, and (n+1), I suggest we get rid of the boolean bias flag and
> make it an integer flag instead, taking either -1 (default), 0, or +1. 
> A boolean flag would be clumsy, since it'd be true for both the n and
> (n+1) cases, and we'd need yet another flag to distinguish between
> these.  And, as others have pointed out, bias=False would be an
> inaccurate description of the std function.
> -- Ed
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Jonathan Taylor                           Tel:   650.723.9230
Dept. of Statistics                       Fax:   650.725.8977
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