From tlumley at uw.edu  Thu May  3 22:41:09 2012
From: tlumley at uw.edu (Thomas Lumley)
Date: Fri, 4 May 2012 08:41:09 +1200
Subject: [Rd] The constant part of the log-likelihood in StructTS
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On Thu, May 3, 2012 at 3:36 AM, Mark Leeds <markleeds2 at gmail.com> wrote:
> Hi Ravi: As far as I know ( well , really read ) and Bert et al can say
> more , the AIC is not dependent on the models being nested as long as the
> sample sizes used are the same when comparing. In some cases, say comparing
> MA(2), AR(1), you have to be careful with sample size usage but there is no
> nesting requirement for AIC atleast, I'm pretty sure.

This is only partly true.  The expected value of the AIC will behave
correctly even if models are non-nested, but there is no general
guarantee that the standard deviation is small,  so AIC need not even
asymptotically lead to optimal model choice for prediction in
arbitrary non-nested models.

Having said that, 'nearly' nested models like these are probably ok.
I believe it's sufficient that all your models are nested in a common
model, with a bound on the degree of freedom difference, but my copy
of Claeskens & Hjort's book on model selection and model averaging is
currently with a student so I can't be definitive.


   -thomas

-- 
Thomas Lumley
Professor of Biostatistics
University of Auckland



[Rd] The constant part of the log-likelihood in StructTS
Thomas Lumley