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AIC

Reasons for AIC:

The expectation value of bias is

\begin{displaymath}
\text{AIC} = -2 \ell(\hat{\theta}) + 2K\end{displaymath} (26)

Exercise: AIC of the least squared fit for a regression model. If $y_n = \sum_{i=1}^{m} a_i x_{ni} + \varepsilon_n$ and $\varepsilon_n \sim N(0, \sigma^2)$[*], find the corresponding AIC number.

Ans. $\text{AIC}_K = N(\log 2\pi \hat{\sigma}_K^2 + 1) + 2(K + 1)$.

Example.Figure 5 shows the normalized asymptotic level changes for the sudden impulses seen at mid-latitude ground magnetometer stations. The trend component (solid line) is estimated based on the hyper-parameter automatically determined in accordance with the AIC minimization procedure [Higuchi, 1991].
  

Figure 5. The normalized aymptotic change in the H component for the sudden impulse events observed by ground stations as a function of local time. The solid line represents the best fit to the data (From Russell and Ginskey, [1995]).

The AIC method also suggests the direction toward selecting the best model by computer calculation.


next up previous contents
Next: AR with AIC Up: Akaike Information Criterion (AIC) Previous: Kullback-Leibler information number and