AICc value derivation (Akaike information criteria for finite samples)

In summary, the conversation discusses the concept of AICc, which is a variation of AIC used in ARIMA. AICc includes an extra penalty term for the number of parameters, which converges to 0 as the sample size increases, making AICc converge to AIC. The individual is seeking a proof for the extra term in AICc in finite samples.
  • #1
mertcan
340
6
Hi everyone, initially let me introduce a concept widely used in ARIMA in the following. $$AICc = AIC + \frac {2k^2+2k} {n-k-1}$$ where n denotes the sample size and k denotes the number of parameters. Thus, AICc is essentially AIC with an extra penalty term for the number of parameters. Note that as n → ∞, the extra penalty term converges to 0, and thus AICc converges to AIC. I have derived AIC value but could provide me with the proof of the extra term $$\frac {2k^2+2k} {n-k-1}$$ particularly used in finite samples?
 
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  • #2
Hi everyone would you mind if I asked why I can not receive any response?
 
  • #3
I am still waiting for your responses?
 

1. What is the AICc value and why is it important?

The AICc value, or Akaike information criteria for finite samples, is a statistical measure used to compare different models and determine which one is the most appropriate for a given dataset. It takes into account both the goodness of fit and the complexity of the model, allowing for a more objective comparison. A lower AICc value indicates a better fit for the data.

2. How is the AICc value derived?

The AICc value is derived by calculating the difference between the maximum likelihood estimate of a model and the number of parameters in that model. This difference is then adjusted for sample size, resulting in the AICc value. The model with the lowest AICc value is considered the best fit for the data.

3. Can the AICc value be used for any type of data?

The AICc value can be used for any type of data, as long as the model being compared is appropriate for the data. It is commonly used in fields such as statistics, ecology, and economics.

4. How does the AICc value differ from other model selection criteria?

The AICc value differs from other model selection criteria, such as the Bayesian information criterion (BIC), in that it takes into account the sample size when penalizing for model complexity. This makes it more suitable for small sample sizes, where the BIC may overfit the data.

5. Are there any limitations to using the AICc value?

Like any statistical measure, the AICc value has its limitations. It assumes that the models being compared are nested, meaning that one model is a simplified version of the other. It also assumes that the data is independent and identically distributed. Additionally, the AICc value may not be appropriate for highly complex models or when the sample size is extremely small.

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