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

Spencer Graves spencer.graves at pdf.com
Fri Jul 6 16:38:31 CEST 2007

      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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