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Date: Tue, 19 Jul 2011 14:55:59 -0700
From: Phil Steitz <phil.steitz@gmail.com>
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Subject: Re: [math] Re: Longley Data
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On 7/18/11 6:31 PM, Greg Sterijevski wrote:
> All,
>
> I have pushed the implementation of the Miller Regression technique, along
> with some tests. I am sure that there are a lot of sharp corners to file
> down and improve. However, I thought it would be prudent to get it out and
> then we can further refine the code.

Thanks!  I just committed the code, with just minor cleanup.  I am
reviewing the article as we speak to verify implementation.  Others
are encouraged to join in here.   We need to complete the javadoc
and decide on exceptions as we stabilize the API here.
>
> On accuracy:
>
> I seem to match all of the digits of longley and wampler data. Filippelli I
> have a very hard time matching except to a tolerance of 1.0e-5. If you look
> at LIMDEP's website:
>
> http://www.limdep.com/features/capabilities/accuracy/linear_regression_3.php
>
> I think that the code I am checking in does a bit better. I am happy about
> that. However, there are some other issues with Filippelli. Namely, one can
> affect the 'accuracy' of your results depending on how you present the data.
> For example, if I generate the high order polynomial naively, x1 = x0 * x0,
> x2  = x0 * x1, ..., x10 = x0 * x9, then I can hit the numbers within 1.0e-5.
> If, however, I generate the Filipelli regressors by multiplying numbers
> whose magnitudes are similar:
>                             x1 = x0 * x0;
>                             x2 = x0 * x1;
>                             x3 = x0 * x2;
>                             x4 = x2 * x2;
>                             x5 = x2 *x3;
>                             x6 = x3 * x3;
> Then I have a very hard time making that 1.0e-5 tolerance.
>
> Does anyone know if there is some article which explains the proper way to
> set up Filippelli's test?

Have not seen anything on this.
>
>
> Speaking to Luc's point, maybe the correct thing to do is to move to
> arbitrary precision. I wanted to avoid this until I was at a deadend.
> Perhaps the time is now....

To generate the x values, yes that would probably be best.


Phil

>
> On tests:
>
> I intend to push 3-4 tests soon. There are 17 tests in the first suite I
> sent in.
>
> -Greg
>


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