[Numpy-discussion] matrix default to column vector?

[josef.pktd at gmail.com]

2009/6/8 Stéfan van der Walt <stefan at sun.ac.za>:
> 2009/6/8 Robert Kern <robert.kern at gmail.com>:
>>> Remember, the example is a **teaching** example.
>>
>> I know. Honestly, I would prefer that teachers skip over the normal
>> equations entirely and move directly to decomposition approaches. If
>> you are going to make them implement least-squares from more basic
>> tools, I think it's more enlightening as a student to start with the
>> SVD than the normal equations.
>
> I agree, and I wish our cirriculum followed that route.  In linear
> algebra, I also don't much like the way eigenvalues are taught, where
> students have to solve characteristic polynomials by hand.  When I
> teach the subject again, I'll pay more attention to these books:
>
> Numerical linear algebra by Lloyd Trefethen
> http://books.google.co.za/books?id=bj-Lu6zjWbEC
>
> (e.g. has SVD in Lecture 4)
>
> Applied Numerical Linear Algebra by James Demmel
> http://books.google.co.za/books?id=lr8cFi-YWnIC
>
> (e.g. has perturbation theory on page 4)
>
> Regards
> Stéfan

Ok, I also have to give my 2 cents

Any basic econometrics textbook warns of multicollinearity. Since,
economists are mostly interested in the parameter estimates, the
covariance matrix needs to have little multicollinearity, otherwise
the standard errors of the parameters will be huge.

If I use automatically pinv or lstsq, then, unless I look at the
condition number and singularities, I get estimates that look pretty
nice, even they have an "arbitrary" choice of the indeterminacy.

So in economics, I never worried too much about the numerical
precision of the inverse, because, if the correlation matrix is close
to singular, the model is misspecified, or needs reparameterization or
the data is useless for the question.

Compared to endogeneity bias for example, or homoscedasticy
assumptions and so on, the numerical problem is pretty small.

This doesn't mean matrix decomposition methods are not useful for
numerical calculations and efficiency, but I don't think the numerical
problem deserves a lot of emphasis in a basic econometrics class.


Josef