Which criterion is designed to be more appropriate for small samples than AIC?

Which criterion is designed to be more appropriate for small samples than AIC?

• A. AIC
• B. AICC
• C. BIC
• D. AIC with small-sample correction

Answer: (B)

When comparing models, information criteria balance how well a model fits the data with how complex it is. In small samples, the standard AIC can under-penalize complexity, leading to overfitting. AICC adds a finite-sample correction to the AIC penalty that depends on both the number of estimated parameters and the sample size. This correction term, 2k(k+1)/(n - k - 1), increases the penalty more when the sample size is small, making it harder for extra parameters to be justified. As the sample size grows, the correction becomes negligible and AICC behaves like AIC, preserving the same decisions in large samples. The other option labeled as a small-sample correction (AIC with small-sample correction) refers to a similar idea (often called AICc), but AICC is the explicitly described corrected form designed for small samples, while BIC uses a different penalty structure and is not specifically a small-sample correction of AIC.

When comparing models, information criteria balance how well a model fits the data with how complex it is. In small samples, the standard AIC can under-penalize complexity, leading to overfitting. AICC adds a finite-sample correction to the AIC penalty that depends on both the number of estimated parameters and the sample size. This correction term, 2k(k+1)/(n - k - 1), increases the penalty more when the sample size is small, making it harder for extra parameters to be justified. As the sample size grows, the correction becomes negligible and AICC behaves like AIC, preserving the same decisions in large samples. The other option labeled as a small-sample correction (AIC with small-sample correction) refers to a similar idea (often called AICc), but AICC is the explicitly described corrected form designed for small samples, while BIC uses a different penalty structure and is not specifically a small-sample correction of AIC.