Re: How to Trap Rogue Data ?

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From: Martin Brown (|||newspam|||_at_nezumi.demon.co.uk)
Date: 07/17/04 

Date: Sat, 17 Jul 2004 13:18:15 +0100

In message <1lhff01hbmo0pjvba9lka2c48qu4tggua4@4ax.com>, bill..
<b@c.com> writes
>
>Thanks for the suggestions
>
>I understand averaging the previous annd next points but what is
>1-Norm fitting?

Classical least squares minimises sum of squares of residuals. = 2-Norm

( y[i] - F(x[i])) ^ 2

1-Norm - minimises sum of absolute magnitude of residuals

| y[i] - F(x[i] |

For the simple case of a small dataset.

2-Norm estimator: Mean = average of all N data values

1-Norm estimator Median = mid point of data histogram

The same trick can be applied to polynomial fitting with robust
statistics. It is much better at ignoring modest numbers of erratic
outliers in noisy data.

Regards, 

-- 
Martin Brown