9.5 Critérios de informação

\(\log\): logaritmo na base \(e \approx\) 2.7182818
\(n\): número de observações
\(k\): número de parâmetros
\(p\): número de variáveis
\(L\): verossimilhança

9.5.1 AIC

Akaike’s information criterion is based on eliminating the asymptotic bias of the maximum likelihood. (Sugiura 1978, 21)

Critério de Informação de Akaike de (Akaike 1974, 215).

\[\begin{equation} AIC = - 2\log(\hat{L}) + 2k \tag{9.21} \end{equation}\]

9.5.2 AICc

Critério de Informação de Akaike corrigido de (Sugiura 1978, 23).

\[\begin{equation} AICc = - 2\log(\hat{L}) + \frac{2n[k-b+(p+1)/2]p}{n-k+b-p-1} \tag{9.21} \end{equation}\]

9.5.3 BIC

Critério de Informação Bayesiano (de Schwarz) de (Schwarz 1978).

\[\begin{equation} BIC = - 2\log(\hat{L}) + \log(n)k \tag{9.22} \end{equation}\]

(Schwarz 1978, 461) sugere, na formulação original, maximizar \(\log(\hat{L}) - \frac{k}{2} \log(n)\). Para mais detalhes recomenda-se (Burnham and Anderson 2004).

9.5.4 HQC

Critério de Informação de Hannan-Quinn

\[\begin{equation} HQC = 2k\ln(\ln(n)) - 2\ln(\hat{L}) \tag{9.23} \end{equation}\]

References

Akaike, Hirotugu. 1974. “A New Look at the Statistical Model Identification.” In Selected Papers of Hirotugu Akaike, 215–22. Springer.
Burnham, Kenneth P, and David R Anderson. 2004. “Multimodel Inference: Understanding AIC and BIC in Model Selection.” Sociological Methods & Research 33 (2): 261–304. http://www.sortie-nd.org/lme/Statistical%20Papers/Burnham_and_Anderson_2004_Multimodel_Inference.pdf.
Schwarz, Gideon. 1978. “Estimating the Dimension of a Model.” The Annals of Statistics, 461–64. https://projecteuclid.org/journals/annals-of-statistics/volume-6/issue-2/Estimating-the-Dimension-of-a-Model/10.1214/aos/1176344136.full.
Sugiura, Nariaki. 1978. “Further Analysis of the Data by Akaike’s Information Criterion and the Finite Corrections: Further Analysis of the Data by Akaike’s.” Communications in Statistics-Theory and Methods 7 (1): 13–26. https://doi.org/10.1080/03610927808827599.