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From Luc Maisonobe <>
Subject Re: [math] Example using EstimationProblem, WeightedMeasurement from apache.commons.math?
Date Tue, 20 Nov 2007 22:19:26 GMT a écrit :
> Thanks for the reply and my apologies for omitting the [math] marker.
> Afa the model goes, I'm not sure how to answer.  What I am doing is
> smoothing a curve using the loess function, and the last step is to use a
> weighted least square regression on each point and its neighborhood.

In addition to my previous message where I gave an implementation based 
on EstimationProblem and WeightedMeasurement as specified, I would like 
to say that in this very simple case, using these classes is probably 
overkill. Low degree polynomials fitting in one dimension only can be 
done very simply with a single loop updating some sums as each sample 
point is added and performing a simple direct computation to retrieve 
the polynomials coefficients at the end of the loop.

EstimationProblem, EstimatedParameters and WeightedParameters are more 
suited for non-linear problems with several different measurements types 
and parameters and complex models. The reference use case for which this 
class was created was to perform spacecraft orbit determination from 
range, range-rate, angular and more exotic measurements with a numerical 
model taking into account several perturbing forces. This requires some 
features that add to the complexity of the classes. I'm not sure using 
such heavyweight component is wise for your case. You may have 
performance issues with them.


>> Hi,
>> First of all, I have added a [math] marker on the subject line. This list
>> is shared among all commons projects and this type of markers help people
>> filter the messages.
>> I will send a usage example on the list in a few hours (late evening,
>> european time), when I'm back home. Would you like to have anything
> special in this example ? For example what kind of model do you want to
> be fitted to the x,ydata ?
>> Luc
>> Selon
>>> Can anybody show me an example of a weighted least squares regression
>>> using classes like EstimationProblem, WeightedMeasurement from
>>> apache.commons.math?
>>> I have data that looks like this: (x,y,weight), e.g.
>>> 1,1,0.2
>>> 2,3, 0.4
>>> 3,2, 1.0
>>> 4,6, 0.8
>>> 5,4, 0.3
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