A new look at the statistical model identification

By Hirotugu Akaike. 1974

The history of the development of statistical hypothesis testing in time series analysis is reviewed briefly and it is pointed out that the hypothesis testing procedure is not adequately defined as the procedure for statistical model identification. The classical maximum likelihood estimation procedure is reviewed and a new estimate minimum information theoretical criterion (AIC) estimate (MAICE) which is designed for the purpose of statistical identification is introduced. When there are several competing models the MAICE is defined by the model and the maximum likelihood estimates of the parameters which give the minimum of AIC defined by AIC = (-2)log-(maximum likelihood) + 2(number of independently adjusted parameters within the model). MAICE provides a versatile procedure for statistical model identification which is free from the ambiguities inherent in the application of conventional hypothesis testing procedure. The practical utility of MAICE in time series analysis is demonstrated with some numerical examples.

Subfields: Evaluation & Benchmarks

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Citations in the corpus

True Few-Shot Learning with Language Models (2021, methodology): “Prior work has developed other model selection criteria such as the Akaike Information Criterion [AIC; 42], Watanabe-Akaike Information Criterion [WAIC; 41], and Mallows’ C p [43].”
Commonsense Knowledge Mining from Pretrained Models (2019, methodology): “] , using the Akaike information criterion of the Gaussian mixture model for evaluation (Akaike, 1974).”
Deep learning in neural networks: An overview (2014, neutral): “…sets (Craven & Wahba, 1979; Eubank, 1988; Golub, Heath, & Wahba, 1979; Hastie & Tibshirani, 1990; Mosteller & Tukey, 1968; Stone, 1974), Akaike’s information criterion and final prediction error (Akaike, 1970, 1973, 1974), or generalized prediction error (Moody, 1992; Moody & Utans, 1994).”
Reinforcement learning (2019, neutral): “• Reward : Once we have I , we determine the parameters θ and we can find the residual as One way to measure the quality of our model is to use the Akaike information criterion AIC (Akaike, 1974).”
On Learning to Think: Algorithmic Information Theory for Novel Combinations of Reinforcement Learning Controllers and Recurrent Neural World Models (2015, background): “2 M ’s Training To decrease bitsM + bitsH , we add a regularizing term to E, to punish excessive complexity [4, 5, 91, 294, 155, 135, 97, 170, 169, 104, 290, 7, 290, 87, 286, 319, 100, 102].”
Community detection in graphs (2009, methodology): “There is no clear-cut recipe to select a model, but a bunch of heuristics, like Akaike Information Criterion (AIC) [310], Bayesian Information Criterion (BIC) [311], Minimum Description Length (MDL) [312,313], MinimumMessage Length (MML) [314], etc.”
An inventory of invasive alien species in China (2012, methodology): “The Akaike Information Criterion (AIC; Akaike 1974) was used for model selection.”
Financial development and economic growth in Greece: an empirical investigation with Granger causality analysis (2004, methodology): “11 Τhis paper follows Engle and Yoo (1987) by using the Akaike information criterion (AIC) (1974), to determine the optimal specification of Equation (2).”
Hyperspectral Subspace Identification (2008, background): “As concluded in [43], these algorithms are the state of the art in hyperspectral signal subspace identification, outperforming the information theoretical criteria approaches, namely, the MDL [40], [41] and the AIC [42].”
New models for estimating the carbon sink capacity of Spanish softwood species (2011, methodology): “In a first step, the best model for each component and species was chosen, based on graphical analysis of residuals and fitting statistics (bias and precision), computing the mean residuals (MRES), root mean square error (RMSE), model efficiency (MEF) (equations 1-3) (Gadow et al., 2001) and the Aka”