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From Phil Steitz <phil.ste...@gmail.com>
Subject Re: [math] Re: Longley Data
Date Tue, 19 Jul 2011 23:32:20 GMT
On 7/19/11 4:13 PM, Greg Sterijevski wrote:
> I think Luc was suggesting implementing the algorithm in extended precision.

I don't really see need for that at this point.  To settle the issue
on results precision, you should start though with high-precision
(or at least precision at the level presented for the X and Y data
by NIST) for the higher X powers.  Doing just that computation in
extended precision is one way to do that.  Of course, that could be
done externally and the data loaded by the test as a file.

Phil
>
> -Greg
>
> On Tue, Jul 19, 2011 at 4:55 PM, Phil Steitz <phil.steitz@gmail.com> wrote:
>
>> 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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