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st: Stata numerical accuracy/precision


From   "Sergiy Radyakin" <serjradyakin@gmail.com>
To   "statalist@hsphsun2.harvard.edu" <statalist@hsphsun2.harvard.edu>
Subject   st: Stata numerical accuracy/precision
Date   Thu, 8 May 2008 11:09:08 -0400

Dear Statalisters,


Q1:

the following results of Stata's accuracy sertification:

http://www.stata.com/support/cert/nist/index.html

indicate that e.g. for linear regression the estimates of coefficients
are guaranteed to be accurate with 6 digits.

In my understanding, "digits" refer to digits in "scientific
notation", rather than "common notation". E.g. I think that if Stata
reports as the answer:

0.00000000034

this value in scientific notation is 3.400e-10, and has only two
"digits", and thus I can trust all of them.

A colleague of mine argues that the "digits" refers to the common
notation, which effectively means that the above result is

0.00000[and here something unknown]

Q2:
the results of accuracy sertification indicate that for linear
regression 6.4 is the lowest precision. This figure comes from a set
of a [limited] number of tests. Is any of these tests designed as the
worst case? Or can it be that for a particular dataset the accuracy is
even lower?

In particular, if the dataset includes figures, where the ratio of max
to min is higher than 1e30?


Any comments to the above are highly welcomed.

Thank you,
   Sergiy Radyakin
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