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Topic: How to minimize a sum
Replies: 6   Last Post: Oct 11, 2013 6:20 AM

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Cristiano

Posts: 48
Registered: 12/7/12
Re: How to minimize a sum
Posted: Oct 10, 2013 4:53 PM
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On 10/10/2013 22:35, James Waldby wrote:
> On Thu, 10 Oct 2013 22:15:46 +0200, Cristiano wrote:
>

>> In this link:
>> http://en.wikipedia.org/wiki/Weighted_arithmetic_mean#Statistical_properties
>>
>> there is the formula sigma(x_bar) = sqrt(...).
>> I need to find the n w's which give the smallest possible sigma(x_bar).
>> Please, could somebody help me?

>
> Your question might not be well-posed. If you are given a set of
> sigma_i values and want to minimize their weighted sum of squared
> values, and weights add up to 1, find the minimum sigma_j,
> set w_j = 1, and set w_i = 0 for i other than j. If weights don't
> have to add up to 1, set them all to zero, which gives sigma(x_bar)=0.


The additional constraint is that all the w's must be greater than 0.

Cristiano




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