MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Akaike's information criterion is a measure of the goodness of fit of an estimated statistical model that accounts for both the fit quality and model complexity. One way to calculate AIC is as follows:

$\mathit{AIC}=2k + n[\ln(\mathit{RSS})]\,$

, where $k$ is the number of parameters in the model and $\mathit{RSS}$ is the residual sum of squares.

Assume two models:

$f_1(x) = ax$


$f_2(x) = \frac{ax}{b + cx} + d \sin(x)$

. Is the number of parameters, $k$, in both the models equal 1?

EDIT In the equations above only $x$ is a variable, while $a$, $b$, $c$ ... are constant parameters

share|cite|improve this question
a,b,c,d...I count four in the second one. – Steve Huntsman Jun 12 '10 at 0:07
Though I guess only three matter... – Steve Huntsman Jun 12 '10 at 6:30
a, b, c, d are constants x is the only variable in the equations – bgbg Jun 12 '10 at 18:16
up vote 0 down vote accepted

The question should be: how many of the parameters need to get estimated based on the data? If three of them were somehow known independently of the data, then I say for present purposes there's only one.

The nonlinearity in $x$ in the $\sin x$ term is not a concern because $f_2(x)$ is linear in $\sin x$ and the parameter is multiplied by that. But I'm wondering whether fitting by minimizing the residual sum of square makes sense when you have nonlinearity in $x$ in the other term.

Akaike's information criterion is one of many used for this purpose that I've heard of, and I'm really not familiar with any of them except to a minor extent that of Mallows.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.