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st: RE: Re: adjusted r square


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Re: adjusted r square
Date   Wed, 21 Feb 2007 12:12:47 -0000

No dispute from me, and this is interesting!

But what is here is par for the course: a mix of 
asymptotic arguments and an appeal to simulations 
for a special case that need not be my model. 

Nick 
n.j.cox@durham.ac.uk 

Kit Baum
 
> This is not merely conjecture. Greene (Econometric Analysis, 
> 5th ed.)  
> p.565 "The Akaike information criterion retains a positive  
> probability of leading to overfitting even as T -> \infty. In  
> contrast, SC(p) [Schwarz or Bayes IC] has been seen to lead to  
> underfitting in some finite sample cases."
> 
> If you do a Monte Carlo simulation in which the true DGP is an AR(p)  
> model, and apply the AIC (pretending that you do not know the  
> appropriate value of p) to determine the lag order, there is a  
> positive probability that AIC will signal a lag length > p. That is  
> what is 'widely agreed' because of that positive bias. Of 
> course, the  
> theory of specification error suggests that you would be better off  
> estimating an overparameterized model than an 
> underparameterized model.
 
 On Feb 21, 2007, at 2:33 AM, Nick wrote:
> 
> >  I regularly read advice such as that AIC is widely agreed
> > to give the wrong answer, to which the reaction has to be, 
> How do they
> > know?

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