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Math Help - how to calculate AIC criteria where model represent pdf with several parametrs

  1. #1
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    Unhappy how to calculate AIC criteria where model represent pdf with several parametrs

    Hello,
    by definition AIC is a simple formula for estimating models,
    AIC=2k-2ln(L), where L -s maximum log likelihood,
    how to calculate AIC when fiitted model represents a PDF with several parameters?
    For example If I want to fit data to a normal distribution,
    I get 2 values of MLE (for mu and sigma).
    Many thanks in advance
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  2. #2
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    I could be wrong, but I believe you can use the MSE as an estimate for \sigma.

    In particular, Kutner, et al., "Applied Linear Statistical Models" (5th ed.) say on page 32 that:

    s^2 = MSE = \frac{n}{n-2}\hat\sigma^2
    Last edited by bryangoodrich; May 25th 2011 at 10:15 AM. Reason: clarity
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  3. #3
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    I'm not sure I understand the issue. Just plug in the MLE's into the likelihood and calculate it. Typically you would use AIC to compare multiple models; if you don't have any alternative models other than the simple normal model then there isn't much else to do.
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