[R] (Statistics question) - Nonlinear regression and simultaneous equation

Spencer Graves
Fri, 06 Jul 2007 14:38:31 -0000

Not all parameters are estimable in some systems of equations like
the classical "errors in X" regression.

      Consistency is an asymptotic property:  On average, as the sample
size increases without bound, a consistent estimator will converge to
what you want.  I'm no expert in asymptotics, but I recall theorems that
suggest that the estimator obtained from a single step in a maximum
likelihood estimation can be consistent -- provided the information is
available in the data and the structure of the model.  The issue is not
whether you use SVM (support vector machine?), FIML (full information
maximum likelihood?) or the 2SLS (2 stage least squares?) or only the
first step.

      Is there information in your data for estimating all the
parameters in your model?  By "information" here, I mean something
like
Fisher information, the negative expectation of the matrix of second
partial derivatives with respect to parameters you want to estimate of a
log(likelihood) for your model.  Is this matrix ill conditioned?  What
happens to its eigenvalues as your hypothetical sample size increases
without bound?

      If these comments do not seem relevant to your question, please
provide more detail of your specific application, preferably including
"commented, minimal, self-contained, reproducible code", as requested
at
the end of every email forwarded by r-help.

      Hope this helps.
      Spencer Graves

adschai at optonline.net wrote:
> Hi,I have a fundamental questions that I'm a bit confused. If any guru
from this circle could help me out, I would really appreciate.I have a system of
equations in which some of the endogs appear on right hand sides of some
equations. To solve this, one needs a technique like 2SLS or FIML to circumvent
inconsistency of the estimated coefficients. My question is that if I apply the
nonlinear regression like SVM regression. Do I still need to worry about
endogeneity? Meaning, what I only need to care is the 1st step of 2SLS. That
would mean that I only need to carry out the SVM regression on all the exogs. Am
I missing anything here? Thank you so much.Regards,- adschai
>
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