statsmodels.tools.eval_measures.aic_sigma¶

statsmodels.tools.eval_measures.aic_sigma(sigma2, nobs, df_modelwc, islog=False)[source]¶

Akaike information criterion

Parameters:¶

sigma2float

estimate of the residual variance or determinant of Sigma_hat in the multivariate case. If islog is true, then it is assumed that sigma is already log-ed, for example logdetSigma.

nobsint

number of observations

df_modelwcint

number of parameters including constant

Returns:¶

aicfloat

information criterion

Notes

A constant has been dropped in comparison to the loglikelihood base information criteria. The information criteria should be used to compare only comparable models.

For example, AIC is defined in terms of the loglikelihood as

\(-2 llf + 2 k\)

in terms of \(\hat{\sigma}^2\)

\(log(\hat{\sigma}^2) + 2 k / n\)

in terms of the determinant of \(\hat{\Sigma}\)

\(log(\|\hat{\Sigma}\|) + 2 k / n\)

Note: In our definition we do not divide by n in the log-likelihood version.

TODO: Latex math

reference for example lecture notes by Herman Bierens

References

https://en.wikipedia.org/wiki/Akaike_information_criterion